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

Algebra ->  Absolute-value -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started


# 1


abs%282x-3%29%2B5=26 Start with the given equation


abs%282x-3%29=21 Subtract 5 from both sides.


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

2x-3=-21 or 2x-3=21 Set the expression 2x-3 equal to the original value 21 and it's opposite -21




Now lets focus on the first equation 2x-3=-21


2x=-21%2B3Add 3 to both sides


2x=-18 Combine like terms on the right side


x=%28-18%29%2F%282%29 Divide both sides by 2 to isolate x



x=-9 Divide






Now lets focus on the second equation 2x-3=21



2x=21%2B3Add 3 to both sides


2x=24 Combine like terms on the right side


x=%2824%29%2F%282%29 Divide both sides by 2 to isolate x



x=12 Divide





So the solutions to abs%282x-3%29%2B5=26 are:

x=-9 and x=12



Notice if we graph y=abs%282x-3%29%2B5 and y=26 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-11%2C30%2C-10%2C30%2Cabs%282x-3%29%2B5%2C26%29 Graph of y=abs%282x-3%29%2B5 (red) and y=26(green)

and we can see the two graphs intersect at x=-9 and x=12. So this verifies our answer.






# 2




abs%283x%2B5%29=11 Start with the given equation


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

3x%2B5=-11 or 3x%2B5=11 Set the expression 3x%2B5 equal to the original value 11 and it's opposite -11




Now lets focus on the first equation 3x%2B5=-11


3x=-11-5Subtract 5 from both sides


3x=-16 Combine like terms on the right side


x=%28-16%29%2F%283%29 Divide both sides by 3 to isolate x



x=-16%2F3 Reduce






Now lets focus on the second equation 3x%2B5=11



3x=11-5Subtract 5 from both sides


3x=6 Combine like terms on the right side


x=%286%29%2F%283%29 Divide both sides by 3 to isolate x



x=2 Divide





So the solutions to abs%283x%2B5%29=11 are:

x=-16%2F3 and x=2



Notice if we graph y=abs%283x%2B5%29 and y=11 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-18%2C4%2C-10%2C12%2Cabs%283x%2B5%29%2C11%29 Graph of y=abs%283x%2B5%29 (red) and y=11(green)

and we can see the two graphs intersect at x=-16%2F3 and x=2. So this verifies our answer.