Question

1. solve and graph the inequality below.

11x - 9 > 13 or -4x - 4 > 8
a. number line: open circles at -3 and 2, arrows left from -3, right from 2
b. number line: open circles at -3 and 2, line between them
c. number line: open circles at -1 and 2, arrows left from -1, right from 2
d. number line: open circles at -1 and 2, line between them

1. solve and graph the inequality below.

2 - (2x - 4) > -4
a. number line: open circle at 5, arrow left
b. number line: open circle at 5, arrow right
c. number line: open circle at 1, arrow left
d. number line: open circle at 1, arrow right

Explanation:

Question 11

Step1: Solve \(11x - 9>13\)

Add 9 to both sides: \(11x>13 + 9\)
\(11x>22\)
Divide by 11: \(x > 2\)

Step2: Solve \(-4x - 4>8\)

Add 4 to both sides: \(-4x>8 + 4\)
\(-4x>12\)
Divide by -4 (reverse inequality): \(x<-3\)

Step3: Analyze the graph

The solution is \(x > 2\) or \(x<-3\). The number line should have open circles at -3 and 2, with shading to the left of -3 and right of 2. This matches option A.

Step1: Simplify the inequality

\(2-(2x - 4)>-4\)
Distribute the negative: \(2-2x + 4>-4\)
Combine like terms: \(6-2x>-4\)

Step2: Solve for \(x\)

Subtract 6: \(-2x>-10\)
Divide by -2 (reverse inequality): \(x < 5\)

Step3: Analyze the graph

The solution is \(x < 5\), so open circle at 5, shading to the left. This matches option D.

Answer:

A. \(\overleftrightarrow{-4\ -3\ -2\ -1\ 0\ 1\ 2\ 3\ 4}\) (open circles at -3 and 2, shading left of -3 and right of 2)

Question 12