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

Question

16-4(k+5)>-64

Answer 1

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 2

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

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.