solve the compound inequality.
9 – 4x ≥ 5 or 4(–1 + x) – 6 ≥ 2

a. x ≥ 1 or x ≥ 3
b. x ≤ 1 or x ≥ 3
c. x ≤ –1 or x ≤ 3
d. x ≥ –1 or x ≥ 3

The compound inequality for 9 – 4x ≥ 5 or 4(–1 + x) – 6 ≥ 2 is:

Option A is correct.

A compound inequality is one that is formed by combining two simple inequalities. They are derived form of fundamental inequalities.

From the question:

The first thing to do is to open the brackets and move the like terms to the same sides.

So,

9 - 5  ≥  4x    or    -4  + 4x - 6   ≥  2

4   ≥ 4x         or      -10 + 4x   ≥  2

4   ≥ 4x         or       4x   ≥ 10 + 2

4   ≥ 4x         or       4x  ≥  12

4x  ≥ 4         or        4x  ≥  12

Divide both sides by 4

x  ≥ 1     or     x  ≥  3

Therefore, the compound inequality of 9 – 4x ≥ 5 or 4(–1 + x) – 6 ≥ 2 is:

x  ≥ 1     or     x  ≥  3

Learn more about compound inequality here:

link

Step-by-step explanation:

9 - 4x > = 5                         or               4(-1 + x) - 6 > = 2

-4x > = 5 - 9                                           -4 + 4x - 6 > = 2

-4x > = -4                                                4x - 10 > = 2

x < = -4/-4                                              4x > = 2 + 10  

x < = 1                                                    4x > = 12

                                                              x > = 12/4

                                                              x > = 3

answer is : B

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