Solving Two-Step Inequalities and Graphing Solutions

The video tutorial explains how to solve and graph two-step inequalities, emphasizing the importance of flipping the inequality sign when multiplying or dividing by a negative number. It provides multiple examples, each demonstrating the step-by-step process of isolating the variable and graphing the solution set on a number line. The tutorial also covers writing inequalities from word problems and solving them.

What is the first step in solving two-step inequalities?

• Flip the inequality sign

• Graph the solution set

• Multiply or divide by the coefficient

• Add or subtract the constant

When must you flip the inequality sign?

• Never

• When multiplying or dividing by a negative number

• When multiplying or dividing by a positive number

• When adding or subtracting a constant

What is the solution for the inequality 2x - 10 > 22?

• x > 16

• x < 32

• x < 16

• x > 32

How do you graph x > 16 on a number line?

• Closed circle on 16, shade left

• Open circle on 16, shade right

• Closed circle on 16, shade right

• Open circle on 16, shade left

What is the correct graph representation for x ≤ -8?

• Closed circle on -8, shade left

• Open circle on -8, shade right

• Closed circle on -8, shade right

• Open circle on -8, shade left

For the inequality 3x + 11 < 2, what is the value of x?

• x > 3

• x < 3

• x > -3

• x < -3

In the inequality -43 ≥ 4x - 3, after adding 3 to both sides, what is the next step?

• Subtract 4 from both sides

• Divide both sides by 4

• Multiply both sides by -1

• Add 43 to both sides

What is the solution set for x divided by -10 < 7?

• x < 70

• x > -70

• x > 70

• x < -70

For the inequality written to represent 'two times a number plus one is less than nine', what is the solution for x?

• x ≥ 4

• x < 4

• x > 4

• x ≤ 4

When solving the inequality '7x + 4 ≥ 39', what is the final value of x?

• x ≥ 5

• x ≤ 5

• x > 5

• x < 5