Question

multiple choice 1 point
solve: -5x - 9 ≤ -4
x ≤ 5
x ≥ 5
x ≤ -1
x ≥ -1

multiple choice 1 point
solve: -1 < 3x + 5 ≤ 14

multiple choice 1 point
solve: 6 ≥ 8 - 2x ≥ -2
1 ≤ x ≤ 7
-1 ≤ x ≤ -5
1 ≤ x ≤ 5
-1 ≤ x ≤ 5

Explanation:

Step1: Isolate the variable in the first - inequality

Add 9 to both sides of $-5x - 9\leq - 4$:
$-5x-9 + 9\leq - 4+9$
$-5x\leq5$

Step2: Solve for $x$

Divide both sides by - 5. Remember to reverse the inequality sign when dividing by a negative number:
$x\geq\frac{5}{-5}$
$x\geq - 1$

Step3: Isolate the variable in the second - inequality $-1\lt3x + 5\leq14$

Subtract 5 from all parts:
$-1-5\lt3x + 5-5\leq14 - 5$
$-6\lt3x\leq9$

Step4: Solve for $x$ in the second - inequality

Divide all parts by 3:
$\frac{-6}{3}\lt\frac{3x}{3}\leq\frac{9}{3}$
$-2\lt x\leq3$

Step5: Isolate the variable in the third - inequality $6\geq8 - 2x\geq - 2$

Subtract 8 from all parts:
$6 - 8\geq8 - 2x-8\geq - 2-8$
$-2\geq - 2x\geq - 10$

Step6: Solve for $x$ in the third - inequality

Divide all parts by - 2 and reverse the inequality signs:
$1\leq x\leq5$

Answer:

1. D. $x\geq - 1$
2. Third option (the one with the line segment from - 2 (open circle) to 3 (closed circle))
3. C. $1\leq x\leq5$