help solve these absolute value equations!?

Question

-5+2|2x-7|= -3

|3x-8|=-2

3|2x-7|=0

thanks!

Answer 1

1) -5+2|2x-7|= -3
2|2x-7| = 2
|2x - 7| = 1
2x-7 = 1 or 2x - 7 = -1
2x = 8, 2x = 6
x = 4, x = 3

2) |3x-8|=-2
No answer. An absolute value can never be negative.

3) 3|2x-7| = 0
Only need one equation because it is equal to 0 and 0 does not have a positive and negative.
2x-7 = 0
2x = 7
x = 3.5

Answer 2

Start by solving for the part that is in the absolute value.
-5+2|2x-7|=-3
add 5 to both sides
2|2x-7|=2
Divide by 2 on both sides
|2x-7|=1
Now you split the problem into 2 parts
if 2x-7 is negative then |2x-7| = -2x+7
if 2x-7 is positive then |2x-7| = 2x-7
This gives you 2x-7 = 1 and -2x+7 = 1
Do the others the same way.

Answer 3

1) 2x-7=0
2x=7
x=3.5
2) 3x-8 =-2 3x-8=2
3x=6 3x=10
x=2 x=3 1/3
3) 2x-7=-3
2x=4
x=2

Answer 4

Subtract 4 from the two aspects: -|3x + 6| = -3 Multiply the two aspects by making use of -a million: |3x + 6| = 3 Absolute values have 2 cases. If 3x + 6 is advantageous, truthfully the fee leaves it unchanged. If 3x + 6 is adverse, truthfully the fee reverses its sign to make it advantageous. advantageous case: 3x + 6 = 3 Subtract 6 from the two aspects: 3x = -3 Divide the two aspects by making use of three x = -a million adverse case: -(3x + 6) = 3 notice the minus sign: -3x - 6 = 3 upload 6 to the two aspects: -3x = 9 Divide the two aspects by making use of -3: x = -3 The suggestions are x = a million and x = -3.

Answer 5

-5 + 2|2x - 7| = -3
2|2x - 7| = 2
|2x - 7| = 1
2x - 7 = 1 or 2x - 7 = -1
2x = 8 or 2x = 6
x = 4 or 3

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|3x - 8| = -2
No Solution, because you can't have a negative absolute value

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3|2x - 7| = 0
|2x - 7| = 0
2x - 7 = 0
2x = 7
x = (7/2)

Answer 6

1) 4,3

2) No solution

3) 7/2

Answer 7

4
2
7/3

Answer 8

a)
2|2x-7|=2
|2x-7|=1
alt.1
2x-7=1
x=4
alt.2
2x-7=-1
x=3
X=4 or x=3
b)Impossible
c)2x-7=0
x=3.5

Answer 9

x=3.5
impossible absolute value cannot be neg
x= and i don't know