Solve the following equations. $3 x - 2 (2 x - 5) = 2 (x + 3) - 8$ . Also, verify.

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Solution

Step 1. Solution of the given equation.
Solve the given equation by Rearranging and combining the like terms:
$\begin{array}{l} 3 x - 2 (2 x - 5) = 2 (x + 3) - 8 \\ \Rightarrow 3 x - 4 x + 10 = 2 x + 6 - 8 \\ \Rightarrow 3 x - 4 x - 2 x = 6 - 8 - 10 \\ \Rightarrow - 3 x = - 12 \\ \Rightarrow x = \frac{12}{3} \\ \Rightarrow x = 4 \end{array}$
Step 2. Verification.
Verify the result by substituting $x = 4$ in the given equation:
$\begin{array}{l} LHS = 3 \times 4 - 2 (2 \times 4 - 5) \\ = 12 - 2 (8 - 5) \\ = 12 - 2 \times 3 \\ = 12 - 6 \\ = 6 \end{array}$
and
$\begin{array}{l} RHS = 2 (4 + 3) - 8 \\ = 2 \times 7 - 8 \\ = 14 - 8 \\ = 6 \end{array}$
Hence, $LHS = RHS$
Hence, the solution of $3 x - 2 (2 x - 5) = 2 (x + 3) - 8$ is $x = 4$ and it is verified.

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