Question

Question 5 (Essay Worth 10 points)

(01.03 MC)
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.

Answer 1

x = 4

Step-by-step explanation:

`\sf \rightarrow √(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 ( 11x)/(11) = (44)/(11)`

simplify the following

`\sf \rightarrow x=4`

Check for Solution:

`\sf \rightarrow √(11(4)+ 5) = 7`

`\sf \rightarrow √(44+ 5) = 7`

`\sf \rightarrow √(49) = 7`

`\sf \rightarrow 7 = 7`

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

Answer 2

x = 4

Step-by-step explanation:

Given:

`√(11x+5)=7`

Square both sides:

`\implies \left(√(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 / 11=44 / 11`

`\implies x=4`