SOLUTION: Please gave me a step by step explanation/answers for the following three problems using the Absolute value of Equation. Thank you for your help 1. |2x-3|+5=26 2. |3x+5|=11

Question 126136: Please gave me a step by step explanation/answers for the following three problems using the Absolute value of Equation. Thank you for your help
1. |2x-3|+5=26
2. |3x+5|=11
3. |3-2/5x|=9
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started

# 1

Start with the given equation

Subtract 5 from both sides.

Break up the absolute value (remember, if you have , then or )

or Set the expression equal to the original value 21 and it's opposite -21

Now lets focus on the first equation

Add 3 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

Now lets focus on the second equation

Add 3 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

So the solutions to are:

and

Notice if we graph and (just set each side equal to y and graph), we get

Graph of (red) and (green)

and we can see the two graphs intersect at and . So this verifies our answer.

# 2

Start with the given equation

Break up the absolute value (remember, if you have , then or )

or Set the expression equal to the original value 11 and it's opposite -11

Now lets focus on the first equation

Subtract 5 from both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Reduce

Now lets focus on the second equation

Subtract 5 from both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Divide

So the solutions to are:

and

Notice if we graph and (just set each side equal to y and graph), we get

Graph of (red) and (green)

and we can see the two graphs intersect at and . So this verifies our answer.

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