Solving One-Variable Inequalities

What is a correct first step in solving the inequality -4(3 – 5x)≥ -6x + 9?

-12 + 20x ≥ -6x + 9

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

B (point three graphed this way —>)

What value of x is in the solution set of -5x – 15 > 10 + 20x?

-1

Solve the inequality.

2(4 + 2x) ≥ 5x + 5?

3

Step 1: -10 + 8x < 6x – 4
Step 2: -10 < -2x – 4
Step 3: -6 < -2x
Step 4: ________

What is the final step in solving the inequality -2(5 – 4x) < 6x – 4?

x>3

Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.

What is the missing step in solving the inequality 5 – 8x < 2x + 3?

Add 8x to both sides of the inequality.

Which is a correct first step in solving 5 – 2x < 8x – 3?

5 < 10x – 3

Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?

C (point -0.5 graphed this way <—)

Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.

1 ≥ 2x E (point on 0.5 and graphed this way —->)

What value of x is in the solution set of 3(x – 4) ≥ 5x + 2?

-10