Question

Show the work to solve |2x+5| -1 < 6 and describe the graph of the solution in a complete sentence.

Answer 1

| 2x + 5 | - 1 < 6

| 2x + 5 | < 6 + 1

| 2x + 5 | < 7

Now, you should split the equation into two (due to the absolute value).
Remember that |x| is the equivilant of x or -x

So solve for:

(2x + 5) < 7

and

-(2x + 5) < 7

The first equation becomes:

2x < 7 - 5

2x < 2 Divide both sides with 2

x < 1


The second equation becomes:

-(2x + 5) < 7

-2x - 5 < 7

-2x < 7 + 5

-2x < 12 Divide both sides with -2

x > -6

Becouse if you multiply or divide both sides of an inequality by a negative number, you MUST reverse the direction of the inequality sign!

Solution:

-6 < x < 1

If you want to see graph of | 2x + 5 | < 7
in google type:
functions graphs online

When you see list of results click on:
rechneronline.de/function-graphs/

When page be open in blue rectangle type:
abs(2x+5)

in gray rectangle type 7

Set:
Range x-axis from -8 to 2

Range y-axis from -2 to 8

and click option Draw

Or go on:
wolfram alpha dot com

then type |2x+5| < 7 and click option =

Also you can construct graph:

For x = -6

| 2x + 5 | = | 2 * ( -6 ) + 5 | = | -12 + 5 | = | -7 | = 7

For x = -5

| 2x + 5 | = | 2 * ( -5 ) + 5 | = | -10 + 5 | = | -5 | = 5

For x = 0

| 2x + 5 | = | 2 * 0 + 5 | = | 0 + 5 | = | 5 | = 5


For x = 1

| 2x + 5 | = | 2 * 1 + 5 | = | 2 + 5 | = | 7 | = 7


etc.