Question

What are the possible values of x if (4x - 5)2 = 49? Check all that apply.
uw we we

Answer 1

x = -
`(1)/(2)`, x = 3

Explanation:

Given

(4x - 5)² = 49 ( take the square root of both sides )

4x - 5 = ±
`√(49)` = ± 7 ( add 5 to both sides )

4x = 5 ± 7, thus

4x = 5 - 7 = - 2 ( divide both sides by 4 )

x =
`(-2)/(4)` = -
`(1)/(2)`

or

4x = 5 + 7 = 12 ( divide both sides by 4 )

x = 3

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

x = -
`(1)/(2)`

left side = (- 2 - 5)² = (- 7)² = 49 = right side ⇒ solution

x = 3

left side = (12 - 5)² = 7² = 49 = right side ⇒ solution