Question

question
select the values that make the inequality ( z geq -2 ) true.
(numbers written in order from least to greatest going across.)
answer

Explanation:

Step1: Understand the inequality

The inequality is \( z \geq -2 \), which means we need to find all values of \( z \) that are greater than or equal to -2.

Step2: Analyze the number line

Looking at the number line, the marked points (from left to right) are -10, -5, -2, 0, 5. We need to check which of these are greater than or equal to -2.

• For -10: \( -10 < -2 \), so it does not satisfy the inequality.
• For -5: \( -5 < -2 \), so it does not satisfy the inequality.
• For -2: \( -2 = -2 \), so it satisfies the inequality.
• For 0: \( 0 > -2 \), so it satisfies the inequality.
• For 5: \( 5 > -2 \), so it satisfies the inequality.

Also, any number to the right of -2 on the number line (including -2 itself) will satisfy the inequality. So the values that make the inequality true are -2, 0, 5, and any numbers greater than -2 (but from the marked points on the number line, we consider -2, 0, 5 and numbers like -1, 1, 2, 3, 4 etc. but since the number line has -2, 0, 5 marked, we can list the marked ones that satisfy and understand the range).

Answer:

The values that make the inequality \( z \geq -2 \) true (from the marked points on the number line) are \(-2\), \(0\), \(5\) and all numbers greater than or equal to \(-2\). If we consider the marked points: \(-2\), \(0\), \(5\) (and also numbers like \(-1\), \(1\), \(2\), \(3\), \(4\) etc. which are greater than or equal to \(-2\)).