Question 1

Solve the inequality $$x - 4 \geq -8$$ and express the solution in interval notation.

Accepted Answer

$$[-4, \infty)$$

Question 2

Which property is used to solve the inequality $$x - 4 \geq -8 by $$adding 4 to both sides?

Accepted Answer

Addition property of inequality

Question 3

If the solution to an inequality is $$x \geq -4$$, which symbol should be used at $$-4$$ when writing the interval notation?

Accepted Answer

Bracket

Question 4

For the inequality $$x \u003c 3$$, how would you write the solution in interval notation?

Accepted Answer

$$(-\infty, 3)$$

Question 5

Which of the following best describes the graph of $$x \geq -4 on a $$number line?

Accepted Answer

Shade to the right of $$-4$$ with a bracket at $$-4$$

Question 6

A medical researcher is analyzing patient data and finds that the number of days a patient recovers is modeled by $$d \geq 5. $$What is the interval notation for the possible recovery days?

Accepted Answer

$$[5, \infty)$$

Question 7

Which of the following statements is TRUE about the solution set for $$x \leq 7$$?

Accepted Answer

The solution set is $$(-\infty, 7]$$

Question 8

A chemical reaction requires the temperature to be at least $$20^	ext{C}. $$Which interval notation represents the acceptable temperature range?

Accepted Answer

$$[20, \infty)$$

Question 9

If $$x \u003e -4$$, which of the following is the correct interval notation for the solution set?

Accepted Answer

$$(-4, \infty)$$

Question 10

A student solves the inequality $$x - 4 \leq -8$$ and gets $$x \leq -4. $$What is the correct interval notation for the solution?

Accepted Answer

$$(-\infty, -4]$$

Question 11

Which of the following is NOT a correct way to represent the solution set for $$x \geq -4$$?

Accepted Answer

$$(-4, \infty)$$

Question 12

A historical event is considered significant if the year is at least 1800. Which interval notation represents the set of significant years?

Accepted Answer

$$[1800, \infty)$$

Question 13

If the solution to an inequality is $$x \u003c -4$$, which symbol should be used at $$-4$$ when writing the interval notation?

Accepted Answer

Parenthesis

Question 14

Which of the following is the correct interval notation for the solution set of $$x \leq 0$$?

Accepted Answer

$$(-\infty, 0]$$

Question 15

A company requires applicants to be at least 18 years old. Which interval notation represents the eligible ages?

Accepted Answer

$$[18, \infty)$$

Solving Linear Inequalities and Graphing Solution Sets

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