Question

Solution of the equation $\frac{2(3x\pm 5)}{4}=3$ is/are:

• A. $x=\frac{1}{2}$
• B. $x=\frac{12}{5}$
• C. $x=\frac{1}{3}$
• D. $x=\frac{11}{3}$

Answer 1

Answer: (C), (D)

$x=\frac{11}{3}$

Given, the equation is $\frac{2(3x\pm 5)}{4}=3.$

Let's simplify the given equation
Step 1: Multiply both the sides by 4
$\Rightarrow \frac{2(3x\pm 5)}{4}\times 4=3\times 4$
$\Rightarrow 2(3x\pm 5)=12$


Step 2: Divide both the sides by 2
$\Rightarrow \frac{2(3x\pm 5)}{2}=\frac{12}{2}$
$\Rightarrow 3x\pm 5=6$

Case 1: Taking positive sign
$\Rightarrow 3x+5=6$
Subtract 5 from both sides
$3x+5-5=6-5\Rightarrow 3x=1$
Divide both the sides by 3
$\Rightarrow \frac{3x}{3}=\frac{1}{3}\Rightarrow x=\frac{1}{3}$

Case 2: Taking negative sign
$\Rightarrow 3x-5=6$
Add 5 to both sides
$3x-5+5=6+5\Rightarrow 3x=11$
Divide both the sides by 3
$\Rightarrow \frac{3x}{3}=\frac{11}{3}\Rightarrow x=\frac{11}{3}$

Hence, solution of the equation $\frac{2(3x\pm 5)}{4}=3$ are $x=\frac{1}{3}$ and $x=\frac{11}{3}.$