The table below shows two equations:

Equation 1 |2x − 3| + 5 = 4
Equation 2 |5x + 3| − 10 = 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 = 2, −3.2.
The solutions to equation 1 are x = 1, 2 and equation 2 has no solution.
The solutions to equation 1 are x = 1, 2 and equation 2 has solutions x = 2, −3.2.

Question

The table below shows two equations:

Equation 1	|2x − 3| + 5 = 4
Equation 2	|5x + 3| − 10 = 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 = 2, −3.2.
The solutions to equation 1 are x = 1, 2 and equation 2 has no solution.
The solutions to equation 1 are x = 1, 2 and equation 2 has solutions x = 2, −3.2.

campbell_st · Answer

what do you know about absolute value...?

anonymous · Answer

It is the number's distance from zero.

campbell_st · Answer

as an example.... can you have 

$$\left| x \right| = -10$$

campbell_st · Answer

that's correct... its distance from zero

anonymous · Answer

But I have no idea how to solve the problems, so I can't answer the question. :c

campbell_st · Answer

ok... so look at the 1st equation... 

$$\left| 2x-3 \right|+5 = 4$$

the 1st step is to subtract 5 from both sides of the equation.

campbell_st · Answer

so you get 

$$\left| 2x -3 \right| = -1$$

this does not have a solution as you can have an absolute value equal to a zero.

anonymous · Answer

So |2x−3|= -1?

campbell_st · Answer

equation 2

add 10 to both sides 

$$\left| 5x + 3 \right| = 13$$

this makes sense... so you now can proceed so you need o solve for the positive and negative 

5x + 3 = 13                     and 5x + 3 = -13

hope it helps

anonymous · Answer

Yes, thank you, I think I got it now.