Question

What is the length of the interval of solutions to the inequality 1≤3-4x≤9?

Answer 1

2

Explanation:

1≤3-4x≤9

subtract 3

1-3≤3-4x-3≤9-3

-2≤-4x≤6

divide by 2

-1≤-2x≤3

multiply by -1

1≥2x≥-3

or

-3≤2x≤1

divide by 2

`-(3)/(2) \leq (2x)/(2) \leq (1)/(2) \\-(3)/(2) \leq x\leq (1)/(2) \\`

length of interval

`=(1)/(2) -((-3)/(2) )\\=(1)/(2) +(3)/(2) \\=(1+3)/(2) \\=(4)/(2) \\=2`

Answer 2

Answer: -3 ≤ x ≤ -1

Explanation:

1 ≤ 3 - 4x ≤ 9

1 + 3 ≤ - 4x ≤ 9 + 3; Add 3 on all sides

4 ≤ -4x ≤ 12

1 ≤ -x ≤ 3; Divide 4 on all sides

-1 ≥ x ≥ -3; Multiply -1 on all sides(FYI: When multiplying or dividing negative numbers in inequalities, make sure to reverse the signs as well)