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Match each inequality to a graph that represents its solutions.

Match each inequality to a graph that represents its solutions.-example-1

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Each inequality should be matched to a graph that represents its solutions as follows;

1. 6x ≤ 3x ↔ graph F.

2. 1/4(x) > -1/2 ↔ graph E.

3. 5x + 4 ≥ 7x ↔ graph B.

4. 8x - 2 < -4(x - 1) ↔ graph D.

5. (4x - 1)/3 > -1 ↔ graph A.

6. 12/5 - x/5 ≤ x ↔ graph C.

Part 1.

Based on the inequalities shown above, we would determine the solution set for each inequality as follows;

6x ≤ 3x

6x - 3x ≤ 0

3x ≤ 0

x ≤ 0/3

x ≤ 0

Therefore, a solid dot would be placed at point 0 on the number line with an arrow that decreases to the left as correctly depicted by graph F.

Part 2.

1/4(x) > -1/2

x > -4/2

x > -2

Therefore, a hollow dot would be placed at point -2 on the number line with an arrow that increases to the right as correctly depicted by graph E.

Part 3.

5x + 4 ≥ 7x

5x - 7x ≤ -4

-2x ≤ -4

x ≤ 4/2

x ≤ 2

Therefore, a solid dot would be placed at point 2 on the number line with an arrow that decreases to the left as correctly depicted by graph B.

Part 4.

8x - 2 < -4(x - 1)

8x - 2 < -4x + 4

8x + 4x < 4 + 2

12x < 6

x < 6/12

x < 1/2

Therefore, a hollow dot would be placed at point 1/2 on the number line with an arrow that decreases to the left as correctly depicted by graph D.

Part 5.

(4x - 1)/3 > -1

4x - 1 > -3

4x > -3 + 1

4x > -2

x > -2/4

x > -1/2

Therefore, a hollow dot would be placed at point -1/2 on the number line with an arrow that increases to the right as correctly depicted by graph A.

Part 6.

12/5 - x/5 ≤ x

12 - x ≤ 5x

5x + x ≥ 12

6x ≥ 12

x ≥ 12/6

x ≥ 2

Therefore, a solid dot would be placed at point 2 on the number line with an arrow that increases to the right as correctly depicted by graph C.

User Matt Martin
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