Solving Multi-step Inequalities in Algebra

What is the first step to solve the inequality 4x + 3 < -1?

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 4

• Divide both sides by 4

After subtracting 3 from both sides of the inequality 4x + 3 < -1, what is the resulting inequality?

• 4x < 2

• 4x < -4

• 4x < -1

• 4x < 1

What is the solution to the inequality 4x < -4?

• x < -1

• x > -1

• x < 1

• x > 1

In the inequality 5x > 8x + 27, what is the first step to isolate x?

• Add 8x to both sides

• Subtract 8x from both sides

• Divide both sides by 5

• Multiply both sides by 5

What is the result of subtracting 8x from both sides of the inequality 5x > 8x + 27?

• 3x > 27

• −3x < 27

• 3x < 27

• −3x > 27

When dividing both sides of an inequality by a negative number, what must you remember to do?

• Add the same number to both sides

• Flip the inequality sign

• Keep the inequality sign the same

• Subtract the same number from both sides

What is the solution to the inequality −3x > 27 after dividing both sides by −3?

• x > 9

• x < 9

• x > −9

• x < −9

In the complex inequality 8x - 5(4x + 1) >= -1 + 2(4x - 3), what is the first step?

• Combine like terms

• Distribute the -5

• Subtract 5 from both sides

• Add 5 to both sides

After distributing and combining like terms in the inequality 8x - 5(4x + 1) >= -1 + 2(4x - 3), what is the resulting inequality?

• 12x + 5 >= −7 + 8x

• −12x + 5 >= −7 + 8x

• 12x − 5 >= −7 + 8x

• −12x − 5 >= −7 + 8x

What is the final solution to the inequality 8x - 5(4x + 1) >= -1 + 2(4x - 3) in interval notation?

• [−∞, 1/10]

• (−∞, 1/10)

• [−∞, 1/10)

• (−∞, 1/10]