Question

Question 5 (Essay Worth 10 points)

Answer 1

Answer:

 x = 4

Explanation:

$\sf \rightarrow \sqrt{11x+ 5} = 7$

square both sides

$\sf \rightarrow 11x+ 5 = 7^2$

simplify the following

$\sf \rightarrow 11x+ 5 = 49$

subtract 5 from both sides

$\sf \rightarrow 11x+ 5 -5 = 49-5$

simplify the following

$\sf \rightarrow 11x = 44$

divide both sides by 11

$\sf \rightarrow \dfrac{ 11x}{11} = \dfrac{44}{11}$

simplify the following

$\sf \rightarrow x=4$

Check for Solution:

$\sf \rightarrow \sqrt{11(4)+ 5} = 7$

$\sf \rightarrow \sqrt{44+ 5} = 7$

$\sf \rightarrow \sqrt{49} = 7$

$\sf \rightarrow 7 = 7$

Hence proved the answer as L.H.S = R.H.S.

Answer 2

Answer:

x = 4

Step-by-step explanation:

Given:

$\sqrt{11x+5}=7$

Square both sides:

$\implies \left(\sqrt{11x+5}\right)^2=7^2$

$\implies 11x+5=49$

Subtract 5 from both sides:

$\implies 11x+5-5=49-5$

$\implies 11x=44$

Divide both sides by 11:

$\implies 11x \div 11=44 \div 11$

$\implies x=4$