```Question 230867
Equation is |3-4x| - 3 <= 8

This means that if the expression within the absolute value sign is positive, then:

3-4x - 3 <= 8

Combine like terms to get:

-4x <= 8

Divide both sides by 4 to get:

-x <= 2

Multiply both sides by -1 to get:

x >= -2

Note that the inequality is reversed when you multiply both sides by -1.

If the expression within the absolute value sign is negative, then:

-(3-4x) - 3 <= 8

This becomes:

-3 + 4x - 3 <= 8

Combine like terms to get:

-6 + 4x <= 8

Add 6 to both sides of the equation to get:

4x <= 8+6 becomes 4x <= 14

Divide both sides of the equation by 4 to get:

x <= 14/4

You have:

x >= -2

and:

x <= 14/4

This is equivalent to -2 <= x <= 14/4

We need to confirm these values are accurate.

We'll take values inside and outside the limits to see what happens.

We'll do:

x = -3 (outside limits)
x = -2 (within limits)
x = 3 (within limits)
x = 14/4 (within limits)
x = 4 (outside limits)

When x = -3, |3-4x| - 3 = |3+12| - 3 = |15| - 3 = 15-3 = 12 > 8 so this is NOT ok as it should be.

When x = -2, |3-4x| - 3 = |3+8| - 3 = |11| - 3 = 11 - 3 = 8 <= 8 so this IS ok as it should be.

When x = 3, |3-4x| - 3 = |3-12| - 3 = |-9| - 3 = 9 - 3 = 6 <= 8 so this IS ok as it should be.

When x = 14/4, |3-4x| - 3 = |3 - 14| - 3 = |-11| - 3 = 11 - 3 = 8 <= 8 so this IS ok as it should be.

When x = 4, |3-4x| - 3 = |3 - 16| - 3 = |-13| - 3 = 13 - 3 = 10 > 8 so this is NOT ok as it should be.

Looks likes these values are good.

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