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Chapter 13

Framing Algebraic Expressions — Exercise 13(C)

Class - 6 Concise Mathematics Selina

Exercise 13(C)

Question 1(i)

Solve :

x+2=6x + 2 = 6

Answer

Solving,

⇒x+2=6 Transposing 2 to R.H.S.,⇒x=6−2⇒x=4\Rightarrow x + 2 = 6\\[1em] \text{ Transposing 2 to R.H.S.,}\\[1em] \Rightarrow x = 6 - 2\\[1em] \Rightarrow x = 4

Hence, x=4\bm{x} = 4.

Question 1(ii)

Solve :

x+6=2x + 6 = 2

Answer

Solving,

⇒x+6=2 Transposing 6 to R.H.S.,⇒x=2−6⇒x=−4\Rightarrow x + 6 = 2\\[1em] \text{ Transposing 6 to R.H.S.,}\\[1em] \Rightarrow x = 2 - 6\\[1em] \Rightarrow x = -4

Hence, x=−4\bm{x} = -4.

Question 1(iii)

Solve :

y+8=5y + 8 = 5

Answer

Solving,

⇒y+8=5 Transposing 8 to R.H.S.,⇒y=5−8⇒y=−3\Rightarrow y + 8 = 5\\[1em] \text{ Transposing 8 to R.H.S.,}\\[1em] \Rightarrow y = 5 - 8\\[1em] \Rightarrow y = -3

Hence, y=−3\bm{y} = -3.

Question 1(iv)

Solve :

x+4=−3x + 4 = -3

Answer

Solving,

⇒x+4=−3 Transposing 4 to R.H.S.,⇒x=−3−4⇒x=−7\Rightarrow x + 4 = -3\\[1em] \text{ Transposing 4 to R.H.S.,}\\[1em] \Rightarrow x = -3 - 4\\[1em] \Rightarrow x = -7

Hence, x=−7\bm{x} = -7.

Question 1(v)

Solve :

y+2=−8y + 2 = -8

Answer

Solving,

⇒y+2=−8 Transposing 2 to R.H.S.,⇒y=−8−2⇒y=−10\Rightarrow y + 2 = -8\\[1em] \text{ Transposing 2 to R.H.S.,}\\[1em] \Rightarrow y = -8 - 2\\[1em] \Rightarrow y = -10

Hence, y=−10\bm{y} = -10.

Question 1(vi)

Solve :

b+2.5=4.2b + 2.5 = 4.2

Answer

Solving,

⇒b+2.5=4.2 Transposing 2.5 to R.H.S.,⇒b=4.2−2.5⇒b=1.7\Rightarrow b + 2.5 = 4.2\\[1em] \text{ Transposing 2.5 to R.H.S.,}\\[1em] \Rightarrow b = 4.2 - 2.5\\[1em] \Rightarrow b = 1.7

Hence, b=1.7\bm{b} = 1.7.

Question 1(vii)

Solve :

p+4.6=8.5p + 4.6 = 8.5

Answer

Solving,

⇒p+4.6=8.5 Transposing 4.6 to R.H.S.,⇒p=8.5−4.6⇒p=3.9\Rightarrow p + 4.6 = 8.5\\[1em] \text{ Transposing 4.6 to R.H.S.,}\\[1em] \Rightarrow p = 8.5 - 4.6\\[1em] \Rightarrow p = 3.9

Hence, p=3.9\bm{p} = 3.9.

Question 1(viii)

Solve :

y+3.2=−6.5y + 3.2 = -6.5

Answer

Solving,

⇒y+3.2=−6.5 Transposing 3.2 to R.H.S.,⇒y=−6.5−3.2⇒y=−9.7\Rightarrow y + 3.2 = -6.5\\[1em] \text{ Transposing 3.2 to R.H.S.,}\\[1em] \Rightarrow y = -6.5 - 3.2\\[1em] \Rightarrow y = -9.7

Hence, y=−9.7\bm{y} = -9.7.

Question 1(ix)

Solve :

a+8.9=−12.6a + 8.9 = -12.6

Answer

Solving,

⇒a+8.9=−12.6 Transposing 8.9 to R.H.S.,⇒a=−12.6−8.9⇒a=−21.5\Rightarrow a + 8.9 = -12.6\\[1em] \text{ Transposing 8.9 to R.H.S.,}\\[1em] \Rightarrow a = -12.6 - 8.9\\[1em] \Rightarrow a = -21.5

Hence, a=−21.5\bm{a} = -21.5.

Question 1(x)

Solve :

x+213=5x + 2\dfrac{1}{3} = 5

Answer

Solving,

⇒x+213=5⇒x+73=5 Transposing 73 to R.H.S.,⇒x=5−73⇒x=15−73⇒x=83=223\Rightarrow x + 2\dfrac{1}{3} = 5\\[1em] \Rightarrow x + \dfrac{7}{3} = 5\\[1em] \text{ Transposing } \dfrac{7}{3} \text{ to R.H.S.,}\\[1em] \Rightarrow x = 5 - \dfrac{7}{3}\\[1em] \Rightarrow x = \dfrac{15 - 7}{3}\\[1em] \Rightarrow x = \dfrac{8}{3} = 2\dfrac{2}{3}

Hence, x=223\bm{x} = 2\dfrac{2}{3}.

Question 1(xi)

Solve :

z+2=415z + 2 = 4\dfrac{1}{5}

Answer

Solving,

⇒z+2=415⇒z+2=215 Transposing 2 to R.H.S.,⇒z=215−2⇒z=21−105⇒z=115=215\Rightarrow z + 2 = 4\dfrac{1}{5}\\[1em] \Rightarrow z + 2 = \dfrac{21}{5}\\[1em] \text{ Transposing 2 to R.H.S.,}\\[1em] \Rightarrow z = \dfrac{21}{5} - 2\\[1em] \Rightarrow z = \dfrac{21 - 10}{5}\\[1em] \Rightarrow z = \dfrac{11}{5} = 2\dfrac{1}{5}

Hence, z=215\bm{z} = 2\dfrac{1}{5}.

Question 1(xii)

Solve :

m+312=414m + 3\dfrac{1}{2} = 4\dfrac{1}{4}

Answer

Solving,

⇒m+312=414⇒m+72=174 Transposing 72 to R.H.S.,⇒m=174−72⇒m=17−144⇒m=34\Rightarrow m + 3\dfrac{1}{2} = 4\dfrac{1}{4}\\[1em] \Rightarrow m + \dfrac{7}{2} = \dfrac{17}{4}\\[1em] \text{ Transposing } \dfrac{7}{2} \text{ to R.H.S.,}\\[1em] \Rightarrow m = \dfrac{17}{4} - \dfrac{7}{2}\\[1em] \Rightarrow m = \dfrac{17 - 14}{4}\\[1em] \Rightarrow m = \dfrac{3}{4}

Hence, m=34\bm{m} = \dfrac{3}{4}.

Question 1(xiii)

Solve :

x+2=114x + 2 = 1\dfrac{1}{4}

Answer

Solving,

⇒x+2=114⇒x+2=54 Transposing 2 to R.H.S.,⇒x=54−2⇒x=5−84⇒x=−34\Rightarrow x + 2 = 1\dfrac{1}{4}\\[1em] \Rightarrow x + 2 = \dfrac{5}{4}\\[1em] \text{ Transposing 2 to R.H.S.,}\\[1em] \Rightarrow x = \dfrac{5}{4} - 2\\[1em] \Rightarrow x = \dfrac{5 - 8}{4}\\[1em] \Rightarrow x = -\dfrac{3}{4}

Hence, x=−34\bm{x} = -\dfrac{3}{4}.

Question 1(xiv)

Solve :

y+513=4y + 5\dfrac{1}{3} = 4

Answer

Solving,

⇒y+513=4⇒y+163=4 Transposing 163 to R.H.S.,⇒y=4−163⇒y=12−163⇒y=−43=−113\Rightarrow y + 5\dfrac{1}{3} = 4\\[1em] \Rightarrow y + \dfrac{16}{3} = 4\\[1em] \text{ Transposing } \dfrac{16}{3} \text{ to R.H.S.,}\\[1em] \Rightarrow y = 4 - \dfrac{16}{3}\\[1em] \Rightarrow y = \dfrac{12 - 16}{3}\\[1em] \Rightarrow y = -\dfrac{4}{3} = -1\dfrac{1}{3}

Hence, y=−113\bm{y} = -1\dfrac{1}{3}.

Question 1(xv)

Solve :

a+315=112a + 3\dfrac{1}{5} = 1\dfrac{1}{2}

Answer

Solving,

⇒a+315=112⇒a+165=32 Transposing 165 to R.H.S.,⇒a=32−165⇒a=15−3210⇒a=−1710=−1710\Rightarrow a + 3\dfrac{1}{5} = 1\dfrac{1}{2}\\[1em] \Rightarrow a + \dfrac{16}{5} = \dfrac{3}{2}\\[1em] \text{ Transposing } \dfrac{16}{5} \text{ to R.H.S.,}\\[1em] \Rightarrow a = \dfrac{3}{2} - \dfrac{16}{5}\\[1em] \Rightarrow a = \dfrac{15 - 32}{10}\\[1em] \Rightarrow a = -\dfrac{17}{10} = -1\dfrac{7}{10}

Hence, a=−1710\bm{a} = -1\dfrac{7}{10}.

Question 2(i)

Solve :

x−3=2x - 3 = 2

Answer

Solving,

⇒x−3=2 Transposing −3 to R.H.S.,⇒x=2+3⇒x=5\Rightarrow x - 3 = 2\\[1em] \text{ Transposing −3 to R.H.S.,}\\[1em] \Rightarrow x = 2 + 3\\[1em] \Rightarrow x = 5

Hence, x=5\bm{x} = 5.

Question 2(ii)

Solve :

m−2=−5m - 2 = -5

Answer

Solving,

⇒m−2=−5 Transposing −2 to R.H.S.,⇒m=−5+2⇒m=−3\Rightarrow m - 2 = -5\\[1em] \text{ Transposing −2 to R.H.S.,}\\[1em] \Rightarrow m = -5 + 2\\[1em] \Rightarrow m = -3

Hence, m=−3\bm{m} = -3.

Question 2(iii)

Solve :

b−5=7b - 5 = 7

Answer

Solving,

⇒b−5=7 Transposing −5 to R.H.S.,⇒b=7+5⇒b=12\Rightarrow b - 5 = 7\\[1em] \text{ Transposing −5 to R.H.S.,}\\[1em] \Rightarrow b = 7 + 5\\[1em] \Rightarrow b = 12

Hence, b=12\bm{b} = 12.

Question 2(iv)

Solve :

a−2.5=−4a - 2.5 = -4

Answer

Solving,

⇒a−2.5=−4 Transposing −2.5 to R.H.S.,⇒a=−4+2.5⇒a=−1.5\Rightarrow a - 2.5 = -4\\[1em] \text{ Transposing −2.5 to R.H.S.,}\\[1em] \Rightarrow a = -4 + 2.5\\[1em] \Rightarrow a = -1.5

Hence, a=−1.5\bm{a} = -1.5.

Question 2(v)

Solve :

y−312=6y - 3\dfrac{1}{2} = 6

Answer

Solving,

⇒y−312=6⇒y−72=6 Transposing −72 to R.H.S.,⇒y=6+72⇒y=12+72⇒y=192=912\Rightarrow y - 3\dfrac{1}{2} = 6\\[1em] \Rightarrow y - \dfrac{7}{2} = 6\\[1em] \text{ Transposing } -\dfrac{7}{2} \text{ to R.H.S.,}\\[1em] \Rightarrow y = 6 + \dfrac{7}{2}\\[1em] \Rightarrow y = \dfrac{12 + 7}{2}\\[1em] \Rightarrow y = \dfrac{19}{2} = 9\dfrac{1}{2}

Hence, y=912\bm{y} = 9\dfrac{1}{2}.

Question 2(vi)

Solve :

z−213=−6z - 2\dfrac{1}{3} = -6

Answer

Solving,

⇒z−213=−6⇒z−73=−6 Transposing −73 to R.H.S.,⇒z=−6+73⇒z=−18+73⇒z=−113=−323\Rightarrow z - 2\dfrac{1}{3} = -6\\[1em] \Rightarrow z - \dfrac{7}{3} = -6\\[1em] \text{ Transposing } -\dfrac{7}{3} \text{ to R.H.S.,}\\[1em] \Rightarrow z = -6 + \dfrac{7}{3}\\[1em] \Rightarrow z = \dfrac{-18 + 7}{3}\\[1em] \Rightarrow z = -\dfrac{11}{3} = -3\dfrac{2}{3}

Hence, z=−323\bm{z} = -3\dfrac{2}{3}.

Question 2(vii)

Solve :

p−5.4=2.7p - 5.4 = 2.7

Answer

Solving,

⇒p−5.4=2.7 Transposing −5.4 to R.H.S.,⇒p=2.7+5.4⇒p=8.1\Rightarrow p - 5.4 = 2.7\\[1em] \text{ Transposing −5.4 to R.H.S.,}\\[1em] \Rightarrow p = 2.7 + 5.4\\[1em] \Rightarrow p = 8.1

Hence, p=8.1\bm{p} = 8.1.

Question 2(viii)

Solve :

x−1.5=−4.9x - 1.5 = -4.9

Answer

Solving,

⇒x−1.5=−4.9 Transposing −1.5 to R.H.S.,⇒x=−4.9+1.5⇒x=−3.4\Rightarrow x - 1.5 = -4.9\\[1em] \text{ Transposing −1.5 to R.H.S.,}\\[1em] \Rightarrow x = -4.9 + 1.5\\[1em] \Rightarrow x = -3.4

Hence, x=−3.4\bm{x} = -3.4.

Question 2(ix)

Solve :

n−4=−415n - 4 = -4\dfrac{1}{5}

Answer

Solving,

⇒n−4=−415⇒n−4=−215 Transposing −4 to R.H.S.,⇒n=−215+4⇒n=−21+205⇒n=−15\Rightarrow n - 4 = -4\dfrac{1}{5}\\[1em] \Rightarrow n - 4 = -\dfrac{21}{5}\\[1em] \text{ Transposing −4 to R.H.S.,}\\[1em] \Rightarrow n = -\dfrac{21}{5} + 4\\[1em] \Rightarrow n = \dfrac{-21 + 20}{5}\\[1em] \Rightarrow n = -\dfrac{1}{5}

Hence, n=−15=−0.2\bm{n} = -\dfrac{1}{5} = -0.2.

Question 3(i)

Solve :

3x=123x = 12

Answer

Solving,

⇒3x=12 Dividing both sides by 3,⇒3x3=123⇒x=4\Rightarrow 3x = 12\\[1em] \text{ Dividing both sides by 3,}\\[1em] \Rightarrow \dfrac{3x}{3} = \dfrac{12}{3}\\[1em] \Rightarrow x = 4

Hence, x=4\bm{x} = 4.

Question 3(ii)

Solve :

2y=92y = 9

Answer

Solving,

⇒2y=9 Dividing both sides by 2,⇒2y2=92⇒y=92=412\Rightarrow 2y = 9\\[1em] \text{ Dividing both sides by 2,}\\[1em] \Rightarrow \dfrac{2y}{2} = \dfrac{9}{2}\\[1em] \Rightarrow y = \dfrac{9}{2} = 4\dfrac{1}{2}

Hence, y=412=4.5\bm{y} = 4\dfrac{1}{2} = 4.5.

Question 3(iii)

Solve :

5z=8.55z = 8.5

Answer

Solving,

⇒5z=8.5 Dividing both sides by 5,⇒5z5=8.55⇒z=1.7\Rightarrow 5z = 8.5\\[1em] \text{ Dividing both sides by 5,}\\[1em] \Rightarrow \dfrac{5z}{5} = \dfrac{8.5}{5}\\[1em] \Rightarrow z = 1.7

Hence, z=1.7\bm{z} = 1.7.

Question 3(iv)

Solve :

2.5m=7.52.5m = 7.5

Answer

Solving,

⇒2.5m=7.5 Dividing both sides by 2.5,⇒2.5m2.5=7.52.5⇒m=3\Rightarrow 2.5m = 7.5\\[1em] \text{ Dividing both sides by 2.5,}\\[1em] \Rightarrow \dfrac{2.5m}{2.5} = \dfrac{7.5}{2.5}\\[1em] \Rightarrow m = 3

Hence, m=3\bm{m} = 3.

Question 3(v)

Solve :

3.2p=163.2p = 16

Answer

Solving,

⇒3.2p=16 Dividing both sides by 3.2,⇒3.2p3.2=163.2⇒p=5\Rightarrow 3.2p = 16\\[1em] \text{ Dividing both sides by 3.2,}\\[1em] \Rightarrow \dfrac{3.2p}{3.2} = \dfrac{16}{3.2}\\[1em] \Rightarrow p = 5

Hence, p=5\bm{p} = 5.

Question 3(vi)

Solve :

2a=4.62a = 4.6

Answer

Solving,

⇒2a=4.6 Dividing both sides by 2,⇒2a2=4.62⇒a=2.3\Rightarrow 2a = 4.6\\[1em] \text{ Dividing both sides by 2,}\\[1em] \Rightarrow \dfrac{2a}{2} = \dfrac{4.6}{2}\\[1em] \Rightarrow a = 2.3

Hence, a=2.3\bm{a} = 2.3.

Question 4(i)

Solve :

x2=5\dfrac{x}{2} = 5

Answer

Solving,

⇒x2=5 Multiplying both sides by 2,⇒x2×2=5×2⇒x=10\Rightarrow \dfrac{x}{2} = 5\\[1em] \text{ Multiplying both sides by 2,}\\[1em] \Rightarrow \dfrac{x}{2} \times 2 = 5 \times 2\\[1em] \Rightarrow x = 10

Hence, x=10\bm{x} = 10.

Question 4(ii)

Solve :

y3=−2\dfrac{y}{3} = -2

Answer

Solving,

⇒y3=−2 Multiplying both sides by 3,⇒y3×3=−2×3⇒y=−6\Rightarrow \dfrac{y}{3} = -2\\[1em] \text{ Multiplying both sides by 3,}\\[1em] \Rightarrow \dfrac{y}{3} \times 3 = -2 \times 3\\[1em] \Rightarrow y = -6

Hence, y=−6\bm{y} = -6.

Question 4(iii)

Solve :

a5=−15\dfrac{a}{5} = -15

Answer

Solving,

⇒a5=−15 Multiplying both sides by 5,⇒a5×5=−15×5⇒a=−75\Rightarrow \dfrac{a}{5} = -15\\[1em] \text{ Multiplying both sides by 5,}\\[1em] \Rightarrow \dfrac{a}{5} \times 5 = -15 \times 5\\[1em] \Rightarrow a = -75

Hence, a=−75\bm{a} = -75.

Question 4(iv)

Solve :

z4=314\dfrac{z}{4} = 3\dfrac{1}{4}

Answer

Solving,

⇒z4=314⇒z4=134 Multiplying both sides by 4,⇒z4×4=134×4⇒z=13\Rightarrow \dfrac{z}{4} = 3\dfrac{1}{4}\\[1em] \Rightarrow \dfrac{z}{4} = \dfrac{13}{4}\\[1em] \text{ Multiplying both sides by 4,}\\[1em] \Rightarrow \dfrac{z}{4} \times 4 = \dfrac{13}{4} \times 4\\[1em] \Rightarrow z = 13

Hence, z=13\bm{z} = 13.

Question 4(v)

Solve :

m6=212\dfrac{m}{6} = 2\dfrac{1}{2}

Answer

Solving,

⇒m6=212⇒m6=52 Multiplying both sides by 6,⇒m6×6=52×6⇒m=5×3=15\Rightarrow \dfrac{m}{6} = 2\dfrac{1}{2}\\[1em] \Rightarrow \dfrac{m}{6} = \dfrac{5}{2}\\[1em] \text{ Multiplying both sides by 6,}\\[1em] \Rightarrow \dfrac{m}{6} \times 6 = \dfrac{5}{2} \times 6\\[1em] \Rightarrow m = 5 \times 3 = 15

Hence, m=15\bm{m} = 15.

Question 4(vi)

Solve :

n7=−2.8\dfrac{n}{7} = -2.8

Answer

Solving,

⇒n7=−2.8 Multiplying both sides by 7,⇒n7×7=−2.8×7⇒n=−19.6\Rightarrow \dfrac{n}{7} = -2.8\\[1em] \text{ Multiplying both sides by 7,}\\[1em] \Rightarrow \dfrac{n}{7} \times 7 = -2.8 \times 7\\[1em] \Rightarrow n = -19.6

Hence, n=−19.6\bm{n} = -19.6.

Question 5(i)

Solve :

−2x=8-2x = 8

Answer

Solving,

⇒−2x=8 Dividing both sides by −2,⇒−2x−2=8−2⇒x=−4\Rightarrow -2x = 8\\[1em] \text{ Dividing both sides by −2,}\\[1em] \Rightarrow \dfrac{-2x}{-2} = \dfrac{8}{-2}\\[1em] \Rightarrow x = -4

Hence, x=−4\bm{x} = -4.

Question 5(ii)

Solve :

−3.5y=14-3.5y = 14

Answer

Solving,

⇒−3.5y=14 Dividing both sides by −3.5,⇒−3.5y−3.5=14−3.5⇒y=−4\Rightarrow -3.5y = 14\\[1em] \text{ Dividing both sides by −3.5,}\\[1em] \Rightarrow \dfrac{-3.5y}{-3.5} = \dfrac{14}{-3.5}\\[1em] \Rightarrow y = -4

Hence, y=−4\bm{y} = -4.

Question 5(iii)

Solve :

−5z=4-5z = 4

Answer

Solving,

⇒−5z=4 Dividing both sides by −5,⇒−5z−5=4−5⇒z=−45=−0.8\Rightarrow -5z = 4\\[1em] \text{ Dividing both sides by −5,}\\[1em] \Rightarrow \dfrac{-5z}{-5} = \dfrac{4}{-5}\\[1em] \Rightarrow z = -\dfrac{4}{5} = -0.8

Hence, z=−45=−0.8\bm{z} = -\dfrac{4}{5} = -0.8.

Question 5(iv)

Solve :

−5=a+3-5 = a + 3

Answer

Solving,

⇒−5=a+3 Transposing 3 to L.H.S.,⇒−5−3=a⇒−8=a\Rightarrow -5 = a + 3\\[1em] \text{ Transposing 3 to L.H.S.,}\\[1em] \Rightarrow -5 - 3 = a\\[1em] \Rightarrow -8 = a

Hence, a=−8\bm{a} = -8.

Question 5(v)

Solve :

2=p+52 = p + 5

Answer

Solving,

⇒2=p+5 Transposing 5 to L.H.S.,⇒2−5=p⇒−3=p\Rightarrow 2 = p + 5\\[1em] \text{ Transposing 5 to L.H.S.,}\\[1em] \Rightarrow 2 - 5 = p\\[1em] \Rightarrow -3 = p

Hence, p=−3\bm{p} = -3.

Question 5(vi)

Solve :

4.5=m−2.74.5 = m - 2.7

Answer

Solving,

⇒4.5=m−2.7 Transposing −2.7 to L.H.S.,⇒4.5+2.7=m⇒7.2=m\Rightarrow 4.5 = m - 2.7\\[1em] \text{ Transposing −2.7 to L.H.S.,}\\[1em] \Rightarrow 4.5 + 2.7 = m\\[1em] \Rightarrow 7.2 = m

Hence, m=7.2\bm{m} = 7.2.

Question 5(vii)

Solve :

325=x−2133\dfrac{2}{5} = x - 2\dfrac{1}{3}

Answer

Solving,

⇒325=x−213⇒175=x−73 Transposing −73 to L.H.S.,⇒175+73=x⇒51+3515=x⇒x=8615=51115\Rightarrow 3\dfrac{2}{5} = x - 2\dfrac{1}{3}\\[1em] \Rightarrow \dfrac{17}{5} = x - \dfrac{7}{3}\\[1em] \text{ Transposing } -\dfrac{7}{3} \text{ to L.H.S.,}\\[1em] \Rightarrow \dfrac{17}{5} + \dfrac{7}{3} = x\\[1em] \Rightarrow \dfrac{51 + 35}{15} = x\\[1em] \Rightarrow x = \dfrac{86}{15} = 5\dfrac{11}{15}

Hence, x=51115\bm{x} = 5\dfrac{11}{15}.

Question 5(viii)

Solve :

5=m+3475 = m + 3\dfrac{4}{7}

Answer

Solving,

⇒5=m+347⇒5=m+257 Transposing 257 to L.H.S.,⇒5−257=m⇒35−257=m⇒m=107=137\Rightarrow 5 = m + 3\dfrac{4}{7}\\[1em] \Rightarrow 5 = m + \dfrac{25}{7}\\[1em] \text{ Transposing } \dfrac{25}{7} \text{ to L.H.S.,}\\[1em] \Rightarrow 5 - \dfrac{25}{7} = m\\[1em] \Rightarrow \dfrac{35 - 25}{7} = m\\[1em] \Rightarrow m = \dfrac{10}{7} = 1\dfrac{3}{7}

Hence, m=137\bm{m} = 1\dfrac{3}{7}.

Question 5(ix)

Solve :

−215=y−4-2\dfrac{1}{5} = y - 4

Answer

Solving,

⇒−215=y−4⇒−115=y−4 Transposing −4 to L.H.S.,⇒−115+4=y⇒−11+205=y⇒y=95=145\Rightarrow -2\dfrac{1}{5} = y - 4\\[1em] \Rightarrow -\dfrac{11}{5} = y - 4\\[1em] \text{ Transposing −4 to L.H.S.,}\\[1em] \Rightarrow -\dfrac{11}{5} + 4 = y\\[1em] \Rightarrow \dfrac{-11 + 20}{5} = y\\[1em] \Rightarrow y = \dfrac{9}{5} = 1\dfrac{4}{5}

Hence, y=145\bm{y} = 1\dfrac{4}{5}.

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