Which of the following is(are) the solutions(s) to |6x - 5|= 7

x = - , x = 2

Step-by-step explanation:

Given

| 6x - 5 | = 7

The absolute value function always returns a positive answer, however the expression inside can be positive or negative.

Thus there will be 2 possible solutions, that is

6x - 5 = 7 OR -(6x - 5) = 7

6x - 5 = 7 ( add 5 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

OR

- (6x - 5) = 7, that is

- 6x + 5 = 7 ( subtract 5 from both sides )

- 6x = 2 ( divide both sides by - 6 )

x = = -

As a check

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

x = 2 : | 6(2) - 5 | = | 12 - 5 | = | 7 | = 7 = right side

x = - : | 6(- ) - 5 | = | - 2 - 5 | = | - 7 | = 7 = right side

The solutions are x = - , x = 2

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft