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Mathematics

If x+56−x+19=x+24\dfrac{x+5}{6} - \dfrac{x+1}{9} = \dfrac{x+2}{4}, then the value of x is

  1. 54\dfrac{5}{4}

  2. 65\dfrac{6}{5}

  3. 76\dfrac{7}{6}

  4. 87\dfrac{8}{7}

Linear Eqns One Variable

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Answer

We have:

=x+56−x+19=x+24⇒3(x+5)−2(x+1)18=x+24⇒(3x+15)−(2x+2)18=x+24⇒3x+15−2x−218=x+24⇒x+1318=x+24⇒4(x+13)=18(x+2)[By cross multiplication]⇒4x+52=18x+36⇒52−36=18x−4x[Transposing +4x to RHS and +36 to LHS]⇒16=14x⇒x=1614⇒x=87\phantom{=} \dfrac{x+5}{6} - \dfrac{x+1}{9} = \dfrac{x+2}{4} \\[1em] \Rightarrow \dfrac{3(x + 5) - 2(x + 1)}{18} = \dfrac{x + 2}{4} \\[1em] \Rightarrow \dfrac{(3x + 15) - (2x + 2)}{18} = \dfrac{x + 2}{4} \\[1em] \Rightarrow \dfrac{3x + 15 - 2x - 2}{18} = \dfrac{x + 2}{4} \\[1em] \Rightarrow \dfrac{x + 13}{18} = \dfrac{x + 2}{4} \\[1em] \Rightarrow 4(x + 13) = 18(x + 2) \quad \text{[By cross multiplication]} \\[1em] \Rightarrow 4x + 52 = 18x + 36 \\[1em] \Rightarrow 52 - 36 = 18x - 4x \quad \text{[Transposing +4x to RHS and +36 to LHS]} \\[1em] \Rightarrow 16 = 14x \\[1em] \Rightarrow x = \dfrac{16}{14} \\[1em] \Rightarrow x = \dfrac{8}{7}

Hence, option 4 is the correct option.

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