Solve the following equation and check your answer:
2x+33−3x−24=1\dfrac{2x + 3}{3}-\dfrac{3x - 2}{4} = 132x+3−43x−2=1
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We have:
=2x+33−3x−24=1⇒4(2x+3)−3(3x−2)12=1⇒8x+12−9x+6=1×12⇒−x+18=12⇒−x=12−18[Transposing +18 to RHS]⇒−x=−6⇒x=6\phantom{=} \dfrac{2x + 3}{3}-\dfrac{3x - 2}{4} = 1 \\[1em] \Rightarrow \dfrac{4(2x + 3) - 3(3x - 2)}{12} = 1 \\[1em] \Rightarrow 8x + 12 - 9x + 6 = 1 \times 12 \\[1em] \Rightarrow -x + 18 = 12 \\[1em] \Rightarrow -x = 12 - 18 \quad \text{[Transposing +18 to RHS]} \\[1em] \Rightarrow -x = -6 \\[1em] \Rightarrow x = 6 \\[1em]=32x+3−43x−2=1⇒124(2x+3)−3(3x−2)=1⇒8x+12−9x+6=1×12⇒−x+18=12⇒−x=12−18[Transposing +18 to RHS]⇒−x=−6⇒x=6
∴ x = 6
Check:
LHS=2x+33−3x−24LHS=153−164LHS=5−4LHS=1RHS=1\text{LHS} = \dfrac{2x + 3}{3} - \dfrac{3x - 2}{4} \\[1em] \phantom{\text{LHS}} = \dfrac{15}{3} - \dfrac{16}{4} \\[1em] \phantom{\text{LHS}} = 5 - 4 \\[1em] \phantom{\text{LHS}} = 1 \\[2em] \text{RHS} = 1LHS=32x+3−43x−2LHS=315−416LHS=5−4LHS=1RHS=1
Hence, LHS = RHS.
Answered By
x - 24% of x = 38
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