Question

1. match each inequality with the graph that represents all the values of x that makes it true.

inequality	graph
x ≤ $1.50	!graph 2(https://example.com/graph2.png)
x ≥ 50	!graph 3(https://example.com/graph3.png)
0 ≥ x	!graph 4(https://example.com/graph4.png)
12 ≤ x	!graph 5(https://example.com/graph5.png)

1. what is the minimum value that will make the inequality b - 2 > 13 true?

Explanation:

Step1: Analyze \(x < 0\)

The values of \(x\) are less than 0. On a number - line, it is represented by an open - circle at 0 and a line extending to the left.

Step2: Analyze \(x\leq1.50\)

The values of \(x\) are less than or equal to 1.50. On a number - line, it is represented by a closed - circle at 1.50 and a line extending to the left.

Step3: Analyze \(x\geq50\)

The values of \(x\) are greater than or equal to 50. On a number - line, it is represented by a closed - circle at 50 and a line extending to the right.

Step4: Analyze \(0\geq x\) (same as \(x\leq0\))

The values of \(x\) are less than or equal to 0. On a number - line, it is represented by a closed - circle at 0 and a line extending to the left.

Step5: Analyze \(12\leq x\) (same as \(x\geq12\))

The values of \(x\) are greater than or equal to 12. On a number - line, it is represented by a closed - circle at 12 and a line extending to the right.

For question 7:

Step1: Solve the inequality \(b - 2>13\)

Add 2 to both sides of the inequality.
\(b-2 + 2>13 + 2\)
\(b>15\)
The smallest integer value of \(b\) that makes the inequality true is \(b = 16\)

Answer:

For question 6:

• \(x < 0\): The graph with an open - circle at 0 and line extending to the left.
• \(x\leq1.50\): The graph with a closed - circle at 1.50 and line extending to the left.
• \(x\geq50\): The graph with a closed - circle at 50 and line extending to the right.
• \(0\geq x\): The graph with a closed - circle at 0 and line extending to the left.
• \(12\leq x\): The graph with a closed - circle at 12 and line extending to the right.

For question 7: 16