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?

A) Equation 1 and equation 2 have no solutions.
B) Equation 1 has no solution, and equation 2 has solutions x = −4, 1.
C) The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.
D) The solutions to equation 1 are x = 3, −1.5, and equation 2 has solutions x = −4, 1.

Answer 1

The easiest way to solve these is to plot them setting each to zero.
Plotting equation 1 yields solutions of 3, -1.5

Plotting equation 2 yields no solution.

So C. is the correct answer.

Answer 2

solve them

remember that
|x|≥0 for any number that you use for x
and

if |a|=b then solve for a such that a=b and a=-b


so


equation 1
|4x-3|-5=4
add 5 to both sides
|4x-3|=9
assume
4x-3=9 and 4x-3=-9
add 3 to both sides
4x=12 and 4x=-6
divide both sides by 4
x=3 and x=-3/2
x=3 and x=-1.5



equation 2
|2x+3|+8=3
minus 8 both sides
|2x+3|=-5
false, can't result in negative with absolute value
no solution


equation 1 has a solution of x=3 and x=-1.5
equation 2 has no solution



C is answer