Question

4
solve: $-3x - 4 geq 5$
$x leq 3$
$x geq 3$
$x geq 12$
$x leq -3$
5
solve: $3x + 7 > 19$
$x > 8\frac{2}{3}$
$x > -4$
$x > 4$
$x < 4$
6
solve: $-9 < x + 2 < 5$
$-7 < x < 3$
$-11 < x < 7$
$-11 < x < 3$
all real numbers
7
solve: $4 < 2x + 4 leq 8$

Explanation:

Step1: Solve the inequality \(-3x - 4\geq5\)

Add \(4\) to both sides: \(-3x-4 + 4\geq5 + 4\), which simplifies to \(-3x\geq9\).
Divide both sides by \(- 3\) and reverse the inequality sign (since dividing by a negative number): \(x\leq - 3\).

Step2: Solve the inequality \(3x + 7>19\)

Subtract \(7\) from both sides: \(3x+7 - 7>19 - 7\), which simplifies to \(3x>12\).
Divide both sides by \(3\): \(x > 4\).

Step3: Solve the compound inequality \(-9

Subtract \(2\) from all parts: \(-9-2

Step4: Solve the compound inequality \(4<2x + 4\leq8\)

Subtract \(4\) from all parts: \(4-4<2x+4 - 4\leq8 - 4\), which gives \(0<2x\leq4\).
Divide all parts by \(2\): \(00\)) and a closed circle at \(2\) (since \(x\leq2\)) with the line segment in between.

Answer:

1. \(x\leq - 3\)
2. \(x > 4\)
3. \(-11
4. The number - line with an open circle at \(0\) and a closed circle at \(2\) and the segment in between (assuming the first of the four number - line options is the correct one based on \(0