Question

1. |2x + 5| = 9?
1) 2,7
2) -2,-7
3) -7,2
4) no solution

Answer 1

Our answer is: 3) -7, 2

`\Large\texttt{Explanation}`

We are asked to solve the following absolute value equation:

|2x + 5| = 9

Recall how the number between the absolute value bars 2x + 5 could be positive or negative. Similarly, 2x + 5 could either be positive or negative.

First let's solve the equation when 2x + 5 is positive -

2x + 5 = 9

2x + 5 - 5 = 9 - 5

2x = 4

2x/2 = 4/2

x = 2

Now we are going to solve the equation when 2x + 5 is negative.

-(2x + 5) = 9

-2x - 5 = 9

-2x = 9 + 5

-2x = 14

x = -7

`\therefore` x could be either 2 or -7.

Answer 2

option 3

Explanation:

given the absolute value equation

| 2x + 5 | = 9

the absolute value function always gives a positive value, however the expression inside the bars can be positive or negative, then the 2 solutions are

2x + 5 = 9 or - (2x + 5) = 9

solving both

2x + 5 = 9 ( subtract 5 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

or

- (2x + 5) = 9 ← distribute parenthesis on left side by - 1

- 2x - 5 = 9 ( add 5 to both sides )

- 2x = 14 ( divide both sides by - 2 )

x = - 7

the solutions are x = 2, - 7