We #160;have:2x+53x+4=3 #8658;2x+53x+4=31 #8658;1 #215;(2x+5)=3 #215;(3x+4) #160; #160; #160; #160; #160; #160; #160; #8658;2x+5=9x+12 ...

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Multiplication of Integers

2 x+53 x+4=3

Question

$\frac{2 x + 5}{3 x + 4} = 3$

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Solution

$\begin{array}{l} We have: \\ \frac{2 x + 5}{3 x + 4} = 3 \\ \Rightarrow \frac{2 x + 5}{3 x + 4} = \frac{3}{1} \\ \Rightarrow 1 \times (2 x + 5) = 3 \times (3 x + 4) \\ \Rightarrow 2 x + 5 = 9 x + 12 \\ \Rightarrow 7 x = - 7 \\ \Rightarrow x = - 1 \\ CHECK: Substituting x = - 1 in the given equation, we get: \\ LHS : \frac{2 x + 5}{3 x + 4} \\ = \frac{2 \times (- 1) + 5}{3 \times (- 1) + 4} \\ = \frac{- 2 + 5}{- 3 + 4} \\ = \frac{3}{1} \\ RHS =3 \\ ∴ LHS = RHS \\ Hence, x = 5 is a solution of the given equation . \\ Verified. \end{array}$

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