Solving Multi-Step Inequalities

The video tutorial covers solving multi-step inequalities, including examples with variables on both sides and using the distributive property. It explains how to solve inequalities, graph solutions on a number line, and verify solutions. Key concepts include flipping inequality symbols when dividing by negative numbers and combining like terms.

What is the first step to isolate the variable in the inequality -8x + 1 ≤ 17?

• Add 8 to both sides

• Subtract 1 from both sides

• Divide by -8

• Multiply by -8

When solving -8x + 1 ≤ 17, what must you remember to do when dividing by a negative number?

• Flip the inequality symbol

• Subtract the same number from both sides

• Keep the inequality symbol the same

• Add the same number to both sides

Is 0 a solution to the inequality x ≥ -2?

• Yes, because 0 is equal to -2

• No, because 0 is less than -2

• No, because 0 is not on the number line

• Yes, because 0 is greater than -2

Is -4 a solution to the inequality x ≥ -2?

• Yes, because -4 is greater than -2

• Yes, because -4 is equal to -2

• No, because -4 is not on the number line

• No, because -4 is less than -2

What is the first step in solving the inequality 2x - 18 < -4x + 16?

• Subtract 16 from both sides

• Add 4x to both sides

• Subtract 2x from both sides

• Add 18 to both sides

After moving all x terms to one side in 2x - 18 < -4x + 16, what is the next step?

• Divide by 6

• Add 18 to both sides

• Subtract 18 from both sides

• Multiply by 6

When using the distributive property in 2x - 6 > 6, what is the first step?

• Multiply both sides by 2

• Add 6 to both sides

• Divide both sides by 2

• Subtract 6 from both sides

What is the solution to the inequality 2x - 6 > 6?

• x > 12

• x < 12

• x < 6

• x > 6

In the inequality 2x + 5 - 9x ≥ -2, what is the result of combining like terms?

• 7x - 5 ≥ -2

• -7x - 5 ≥ -2

• 7x + 5 ≥ -2

• -7x + 5 ≥ -2

What is the final solution to the inequality 2x + 5 - 9x ≥ -2?

• x ≥ 1

• x ≤ 1

• x ≤ -1

• x ≥ -1