Answer:
B
Step-by-step explanation:
the absolute value function always gives a positive result
However, the value inside can be positive or negative, that is
5x + 30 = 10x or - (5x + 30) = 10x
solving both
5x + 30 = 10x (subtract 5x from both sides )
30 = 5x ( divide both sides by 5 )
6 = x
or
- (5x + 30) = 10x
- 5x - 30 = 10x ( add 5x to both sides )
- 30 = 15x ( divide both sides by 15 )
- 2 = x
As a check
substitute these values into the equation and if both sides are equal then it is a solution.
x = 6
left side = | 5(6) + 30 | = | 30 + 30 | = | 60| = 60
right side = 10(6) = 60
Then x = 6 is a solution
x = - 2
left side = | 5(- 2) + 30 | = | - 10 + 30 | = | 20 | = 20
right side = 10(- 2) = - 20 ≠ 20
Thus x = - 2 is an extraneous solution
