Question

Solve the equation:
5|2x-7|=20

Answer 1

x =
`(11)/(2)`,
`(3)/(2)`

Explanation:

First, isolate the absolute value:

5|2x - 7| = 20

divide both sides by 5:

|2x - 7| = 4

break into 2 equations:

2x - 7 = 4, 2x - 7 = -4

solve both equations and collect solutions:

2x = 11, 2x = 3

x =
`(11)/(2)`,
`(3)/(2)`

Answer 2

x=11/2,3/2

Explanation:

Given equation:

5|2x-7|=20

=> |2x-7| = 20/5 = 4

Since the left hand side is an absolute value, the equation can be expressed in two alternate forms.

The two possible scenarios are:

1) 2x-7 = 4 or 2) 2x-7 = -4

Solving these two equations individually:

Equation 1:

1) 2x-7 = 4

=> 2x = 4+7=11

=> x= 11/2

2) 2x-7 = -4

=> 2x = 7-4 = 3

=> x=3/2

Hence the required values of x are 11/2,3/2