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i am working on Absolute value and i need help here are the questions

  1. | 2x |=4

  2. | x-3 |=7

  3. | 2x+5 |=21

  4. 3 |x+4|= 24

  5. | x+2 | = 2x+4

6.| x+7 |=0

  1. 2 | x+1 | - 3 +17

Verified Answer :

1) 2x = +/- 4 so x = +/- 2

2) x-3 = 7  OR x - 3 = -7
so x = 10 or x = -4

3)2x + 5 = 21 OR 2x + 5 = -21
so x = 8 or x = -13

4) x + 4 = 6 OR x + 4 = -6
so x = 2 or x = -10

5) x + 2 = -(2x+4) OR x + 2 = 2x + 4
x = -2 or x = -6

6) x + 7 =  0
x = -7

7) you forgot the equal sign somewhere in this problem

apologiabiology

remember
if you have |a|=b
solve for a=b and a=-b

1. | 2x |=4
assume 2x=4 and 2x=-4
divide by 2
x=2 and -2

  1. | x-3 |=7
    assume x-3=7 and - 7
    add 3 to both sides of each equation
    x=10 and -4

  2. | 2x+5 |=21
    assume 2x+5=21 and 2x+5=-21
    minus 5 both sides
    2x=16 and 2x=-26
    divide by 2
    x=8 and x=-13

  3. 3 |x+4|= 24
    divide both sides by 3
    |x+4|=8
    assume that x+4=8 and x+4=-8
    minus 4 both sides
    x=4 and x=-12

  4. | x+2 | = 2x+4
    assume
    x+2=2x+4 and x+2=-(2x+4)=-2x-4
    minus 2 both sides
    x=2x+4 and x=-2x-6
    first one, minus 2x both sides and multiply by -1
    2nd one, add 2x to both sides and divide by 3
    x=-4 and -2

6.| x+7 |=0
x+7=0
minus 7
x=-7

  1. 2 | x+1 | - 3 =17


add 3 to both sides
2|x+1|=20
divide both sides by 2
|x+1|=10
assume
x+1=10 and x+1=-10
minus 1 both sides
x=9 and -11





1. x=-2 and x=2
2. x=-4 and x=10
3. x=-13 and x=8
4. x=-12 and x=4
5. x=-4 and -2
6. x=-7
7. x=-11 and x=9

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