Question

SOLVING ABSOLUTE VALUE EQUATION

Answer 1

Answer:

1. x=27

2. x=11 or x=-7

3. x=4

4. x=1 or $x=\frac{1}{3}$

5. x=12

6. x=11 or x=-1

7. x=8

8. x=3 or x=1

9. $x=\frac{13}{2}$ or x=-4

10.x=7 or x=1

Step-by-step explanation:

For the first 8, the absolute value portion is just substituted in for x, so we can skip some of the repeated work that would occur in these. For the absolute value problems, there are two solutions each. When you remove an absolute value, you have to add a plus or minus to each side and solve for each.

1. $5x+9=144\\5x=135\\x=27$

2. $|3x-6|=27\\3x-6=27\\3x=33\\x=11\\\\3x-6=-27\\3x=-27\\x= -7$

3. $\frac{x}{7-3} =1\\\frac{x}{4} =1\\x=4$

4. $|12x-8|=4\\12x-8=4\\12x=12\\x=1\\\\12x-8=-4\\12x=4\\x=\frac{4}{12} \\\\x=\frac{1}{3}$

5. $\frac{2}{3}x-11=-3\\\frac{2}{3}x=8\\x=\frac{24}{2}\\ x=12$

6. $|2x-10|=12\\2x-10=12\\2x=22\\x=11\\\\2x-10=-12\\2x=-2\\x=-1$

7. $\frac{4x-5}{3} =9\\4x-5=27\\4x=32\\x=8$

8. $|8x-16|=8\\8x-16=8\\8x=24\\x=3\\\\8x-16=-8\\8x=8\\x=1$

9. $|4x-5| +15=36\\|4x-5|=21\\4x-5=21\\4x=26\\x=\frac{26}{4} \\x=\frac{13}{2} \\\\4x-5=-21\\4x=-16\\x=-4$

10. $6|3x-12|-5=49\\6|3x-12|=54\\|3x-12|=9\\3x-12=9\\3x=21\\x=7\\\\3x-12=-9\\3x=3\\x=1$