Question

The table below shows two equations:

Equation 1 |4x − 3|− 5 = 4
Equation 2 |2x + 3| + 8 = 3

Which statement is true about the solution to the two equations?
Equation 1 and equation 2 have no solutions.
Equation 1 has no solution, and equation 2 has solutions x = −4, 1.
The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.
The solutions to equation 1 are x = 3, −1.5, and equation 2 has solutions x = −4, 1.

Answer 1

(1) has solutions x = 3, x= - 1.5 and (2) has no solution

solving each equation

(1)

add 5 to both sides

|4x - 3 | = 9 ( remove bars from absolute value )

4x - 3 = 9 or 4x - 3 = - 9 ( by definition )

4x = 9 + 3 = 12 or 4x = - 9 + 3 = - 6

x = 3 or x = - 1.5

(2)

subtract 8 from both sides

|2x + 3 | = - 5

the absolute value cannot be equal to a negative quantity

thus |2x + 3 | = - 5 has no solution

Answer 2

The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.

Explanation:

Rearranging the two equations, you get ...

• |4x -3| = 9 . . . . . has two solutions
• |2x +3| = -5 . . . . has no solutions (an absolute value cannot be negative)

The above-listed answer is the only one that matches these solution counts.

_____

Testing the above values of x reveals they are, indeed, solutions to Equation 1.