Question 1

Which property allows you to eliminate a common factor from both sides of an inequality, such as dividing both sides by 5 in $$5(3x+10)\u003e5$$?

Accepted Answer

The multiplication property of inequality

Question 2

What is the solution set for the inequality $$5(3x+10)\u003e5$$ written in interval notation?

Accepted Answer

$$(-3, \infty)$$

Question 3

After applying the distributive property to $$5(3x+10)\u003e5$$, what is the resulting inequality?

Accepted Answer

$$15x+50\u003e5$$

Question 4

If you subtract 10 from both sides of $$3x+10\u003e1$$, which property are you using?

Accepted Answer

The addition property of inequality

Question 5

What is the solution to $$3x\u003e-9$$?

Accepted Answer

$$x\u003e-3$$

Question 6

Which interval notation correctly represents all real numbers greater than $$-3$$?

Accepted Answer

$$(-3, \infty)$$

Question 7

If you multiply both sides of an inequality by a negative number, what happens to the inequality sign?

Accepted Answer

It reverses direction

Question 8

Which property is used when dividing both sides of $$3x\u003e-9 by 3$$?

Accepted Answer

The multiplication property of inequality

Question 9

In the context of interval notation, which symbol is used to indicate that an endpoint is not included?

Accepted Answer

Parenthesis

Question 10

Given the inequality $$x\u003e-3$$, which of the following values is NOT in the solution set?

Accepted Answer

$$-3$$

Question 11

A real-world scenario: If a company requires that the number of products $$x$$ produced must be greater than $$-3 to $$avoid losses, which interval represents the possible values for $$x$$?

Accepted Answer

$$(-3, \infty)$$

Question 12

If you have the inequality $$a\u003cb$$ and multiply both sides by a positive number $$c$$, what is the resulting inequality?

Accepted Answer

$$ac\u003cbc$$

Question 13

Which property allows you to add or subtract the same value from both sides of an inequality without changing the solution set?

Accepted Answer

The addition property of inequality

Question 14

If $$x$$ must be greater than $$-3$$ but not equal to $$-3$$, which notation best describes the solution set?

Accepted Answer

$$(-3, \infty)$$

Question 15

Which step is necessary to isolate $$x in $$the inequality $$3x+10\u003e1$$?

Accepted Answer

Subtract 10 from both sides

Question 16

If you have $$a\u003cb$$ and multiply both sides by a negative number $$c$$, what is the resulting inequality?

Accepted Answer

$$ac\u003ebc$$

Question 17

Which property is used to remove grouping symbols in $$5(3x+10)\u003e5$$?

Accepted Answer

The distributive property

Question 18

If the solution to an inequality is $$x\u003e-3$$, which of the following is a correct way to express the solution set?

Accepted Answer

$$\{x\mid x\u003e-3\}$$

Question 19

Why is a parenthesis used at $$-3 in $$the interval $$(-3, \infty)$$?

Accepted Answer

Because $$-3 is $$not included in the solution set

Question 20

Which of the following best describes the solution set for $$x\u003e-3 in $$set-builder notation?

Accepted Answer

$$\{x\mid x\u003e-3\}$$

Solving Linear Inequalities and Expressing Solutions in Interval Notation

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