Question 1

Solve the inequality $$5x + 2 \geq 12. $$What is the solution?

Accepted Answer

$$x \geq 3$$

Question 2

Which answer choice below is the graph of $$x \leq 3$$?

Accepted Answer

A number line with a filled circle at 3 and shading to the left

Question 3

Simplify $$3x + x + 5x + 2x + x.$$

Accepted Answer

$$12x$$

Question 4

A medical researcher is analyzing the inequality $$5x + 2 \geq 12 to $$determine the minimum dosage (in mg) of a drug required for effectiveness. If $$x$$ represents the dosage, what is the minimum effective dosage?

Accepted Answer

$$x = 3$$ 	ext{ mg}$

Question 5

Which of the following represents the solution set for $$x \leq 3 on a $$number line?

Accepted Answer

A filled circle at 3 with shading to the left

Question 6

If $$x$$ represents the number of hours a student studies and the requirement is $$5x + 2 \geq 12$$, what is the minimum number of hours the student must study?

Accepted Answer

$$x \geq 3$$

Question 7

Which of the following is the correct simplification of $$3x + x + 5x + 2x + x$$?

Accepted Answer

$$12x$$

Question 8

A company requires that the number of products $$x$$ produced must satisfy $$5x + 2 \geq 12. $$What is the minimum number of products that must be produced?

Accepted Answer

$$x = 3$$

Question 9

Which graph correctly represents the solution to $$x \leq 3$$?

Accepted Answer

A number line with a filled circle at 3 and shading to the left

Question 10

If $$x is $$the number of tickets sold and the requirement is $$5x + 2 \geq 12$$, what is the minimum number of tickets that must be sold?

Accepted Answer

$$x = 3$$

Solving Linear Inequalities and Graphing Solutions on a Number Line

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