Question

Solve for $x:$
$\frac{2(2x+3)}{4}=6$

• A. $x=\frac{9}{2}$
• B. $x=\frac{3}{4}$
• C. $x=\frac{1}{2}$
• D. $x=\frac{5}{4}$

Answer 1

The correct option is A $x=\frac{9}{2}$

Given, the equation is $\frac{2(2x+3)}{4}=6.$

Step 1: To simplify the equation, multiply both the sides by 4
$\Rightarrow \frac{2(2x+3)}{4}\times 4=6\times 4$
$\Rightarrow 2(2x+3)=24$

Step 2: Divide both the sides by 2
$\Rightarrow \frac{2(2x+3)}{2}=\frac{24}{2}$
$\Rightarrow 2x+3=12$

Step 3: Subtract 3 from both sides of the equation in order to remove $3$ on the left hand side.
$\Rightarrow 2x+3-3=12-3$
$\Rightarrow 2x=9$

Step 4: Divide both the sides by 2
$\Rightarrow \frac{2x}{2}=\frac{9}{2}$
$\Rightarrow x=\frac{9}{2}$

Hence, solution of the equation $\frac{2(2x+3)}{4}=6$ is $x=\frac{9}{2}.$