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? (1 point) 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.

Answer 1

We have been given two equations

1 |2x − 3| + 5 = 4 and |5x + 3| − 10 = 3

Let's solve both

solution for 1 |2x − 3| + 5 = 4

1 |2x − 3| = 4 -5

1 |2x − 3| = -1

|2x − 3| = -1

We know that absolute functions output is always positive number. while here we have -1 which is negative and not possible.

So there is NO Solution for this equation.

solution for |5x + 3| − 10 = 3

|5x + 3| − 10 = 3

|5x + 3| = 3+10

|5x + 3| = 13

5x + 3 = +13  or 5x + 3 = -13  

5x  = +13-3  or 5x  = -13 -3

5x  = 10  or 5x  = -16

x=2 or x=-16/5=-3.2

Now we can easily select correct option:

Equation 1 and equation 2 have no solutions. {FALSE}

Equation 1 has no solution and equation 2 has solutions x = 2, −3.2. {TRUE}

The solutions to equation 1 are x = 1, 2 and equation 2 has no solution. {FALSE}

The solutions to equation 1 are x = 1, 2 and equation 2 has solutions x = 2, −3.2.{FALSE}