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Solve the compound inequality for [tex]x[/tex]:

[tex]\[ 5x - 7 \geq 8 \text{ or } 4x + 4 \ \textless \ -20 \][/tex]

Select one:
a. [tex]x \geq 3[/tex] or [tex]x \ \textless \ -6[/tex]
b. [tex]x \geq \frac{1}{5}[/tex] or [tex]x \ \textless \ -4[/tex]
c. [tex]x \ \textless \ -4[/tex]
d. [tex]x \geq 5[/tex] or [tex]x \ \textgreater \ 6[/tex]

Sagot :

GinnyAnsweridn
To solve the compound inequality [tex]\(5x - 7 \geq 8\)[/tex] or [tex]\(4x + 4 < -20\)[/tex], we need to solve each inequality separately and then combine the solutions using the logical "or."

### Step 1: Solve [tex]\(5x - 7 \geq 8\)[/tex]

1. Isolate [tex]\(x\)[/tex]:
[tex]\[ 5x - 7 \geq 8 \][/tex]

2. Add 7 to both sides:
[tex]\[ 5x \geq 15 \][/tex]

3. Divide both sides by 5:
[tex]\[ x \geq 3 \][/tex]

### Step 2: Solve [tex]\(4x + 4 < -20\)[/tex]

1. Isolate [tex]\(x\)[/tex]:
[tex]\[ 4x + 4 < -20 \][/tex]

2. Subtract 4 from both sides:
[tex]\[ 4x < -24 \][/tex]

3. Divide both sides by 4:
[tex]\[ x < -6 \][/tex]

### Step 3: Combine the solutions

The solutions to the inequalities are:

1. [tex]\(x \geq 3\)[/tex] from the first inequality.
2. [tex]\(x < -6\)[/tex] from the second inequality.

Combining these, we get [tex]\(x \geq 3\)[/tex] or [tex]\(x < -6\)[/tex].

Thus, the correct answer is:
a. [tex]\(x \geq 3\)[/tex] or [tex]\(x < -6\)[/tex].
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