Question

Solve the inequality. You must show ALL work to earn full credit.

16-4(k+5)>-64

Answer 1

3(x+6)>_4(2x-7)+6

Answer 2

To solve the inequality \( 16 - 4(k + 5) > -64 \), we will follow these steps:

1. **Distribute -4** across \( (k + 5) \):
\[
16 - 4k - 20 > -64
\]

2. **Combine like terms** on the left side:
\[
-4k - 4 > -64
\]

3. **Add 4** to both sides to isolate the term with \( k \):
\[
-4k > -64 + 4
\]
\[
-4k > -60
\]

4. **Divide** both sides by -4. Remember that when dividing by a negative number, we reverse the inequality sign:
\[
k < \frac{-60}{-4}
\]
\[
k < 15
\]

Thus, the solution to the inequality is:
\[
\boxed{k < 15}
\]

This means that any value of \( k \) that is less than 15 will satisfy the original inequality.

Answer 3

To solve the inequality \( 3(x + 6) \geq 4(2x - 7) + 6 \), we will follow these steps carefully:

1. **Distribute** on both sides:

Left Side:
\[
3(x + 6) = 3x + 18
\]

Right Side:
\[
4(2x - 7) + 6 = 8x - 28 + 6 = 8x - 22
\]

Thus, the inequality becomes:
\[
3x + 18 \geq 8x - 22
\]

2. **Rearrange** the inequality by getting all terms involving \( x \) on one side and constants on the other. First, we'll subtract \( 3x \) from both sides:
\[
18 \geq 8x - 3x - 22
\]
This simplifies to:
\[
18 \geq 5x - 22
\]

3. **Add 22** to both sides:
\[
18 + 22 \geq 5x
\]
Simplifying gives:
\[
40 \geq 5x
\]

4. **Divide** both sides by 5:
\[
\frac{40}{5} \geq x
\]
Which simplifies to:
\[
8 \geq x
\]

This can also be written as:
\[
x \leq 8
\]

Thus, the solution to the inequality is:
\[
\boxed{x \leq 8}
\]

This means that any value of \( x \) that is less than or equal to 8 will satisfy the original inequality.