Question

Solution of the equation $\frac{\pm 5(4x-2)}{7}=10$ is/are:

• A. $x=-3$
• B. $x=4$
• C. $x=-4$
• D. $x=3$

Answer 1

Answer: (A), (B)

$x=4$

Given, the equation is $\frac{\pm 5(4x-2)}{7}=10.$

Step 1: Multiply both the sides by 7
$\Rightarrow \frac{\pm 5(4x-2)}{7}\times 7=10\times 7$
$\Rightarrow \pm 5(4x-2)=70$

Case 1: Taking positive sign
$\Rightarrow 5(4x-2)=70$
Simplify the left hand side of equation, we get
$\Rightarrow 5\times 4x-5\times 2=70\Rightarrow 20x-10=70$
Add 10 to both sides
$\Rightarrow 20x-10+10=70+10\Rightarrow 20x=80$
Divide both the sides by 20
$\Rightarrow \frac{20x}{20}=\frac{80}{20}\Rightarrow x=\frac{20\times 4}{20}$
$\Rightarrow x=4$

Case 2: Taking negative sign
$\Rightarrow -5(4x-2)=70$
Simplify the left hand side of equation, we get
$\Rightarrow -5\times 4x-(-5\times 2)=70\Rightarrow -20x-(-10)=70\Rightarrow -20x+10=70$
Subtract 10 from both sides
$\Rightarrow -20x+10-10=70-10\Rightarrow -20x=60$
Divide both the sides by -20
$\Rightarrow \frac{-20x}{-20}=\frac{60}{-20}\Rightarrow x=-3$

Hence, solution of the equation $\frac{\pm 5(4x-2)}{7}=10$ are $x=4$ and $x=-3.$