Question 130145: Hello, not really sure about absolute value, trying to get my information and help from internet websites. I believe the answer to number one is -19,19. I have to show both solutions to the equation that works, so I believe that is correct....Thank you!
|x+1|+20
|2m-4|=10
|2/3t+1|=8
|2x-3|<7
|5t-1|>9
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! Solving absolute value equations can be tricky, but checking the solution is pretty simple. Let's check yours. If x=19, |x+1|=20 means|19+1|=20, which means |20|=20, which is true. But if x=-19, then |x+1|=20 means|-19+1|=20, which means |-18|=20, which is false. So you are right about 19, but not -19. I am betting you solved this by pretending the absolute value wasn't there, solving for x, and adding +/-. But the problem is not just x is in the absolute value. The absolute of x+1 is 20 means x+1=+/-20. So take these situations separately. If x+1=20, then x=19. But if x+1=-20, then x=-21. So x=-21,19. For the third one, 2/3t+1=8 or 2/3t+1=-8. First case: 2/3t=7, t=7*(3/2)=10.5. Second case: 2/3t=-9, t=-9*(3/2)=-13.5.
So t=-13.5,10.5
For inequalities, pretend it is an equation and get your two solutions. Then the answer is either between the two solutions or on opposite sides. You need to test a point to find out. I'll do the last one as an example.
Pretend |5t-1|>9 says |5t-1|=9. So 5t-1=+/-9. If 5t-1=9, then 5t=10, t=2. If 5t-1=-9, 5t=-8, t=-8/5, t=-1.6. So t=-1.6, 2.
But there was an inequality sign. We have 2 options now. The solution is either (1) t is between -1.6 and , or (2) t is less than -1.6 or greater than 2. See if t=0 satisfies the inequality. |5t-1|>9 means |5(0)-1|>9, so |-1|>9, so 1>9. This is false. So option 2 must be the correct one. test with -2 and 3. If t=-2, |5t-1|>9 means |-10-1|>9, so |-11|>9, so 11>9. This is true. If t=3, |5t-1|>9 means |15-1|>9, so 14>9. This is also true. So -1.6>t or t>2.
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