Solve the following inequality and graph the solution.

Question

4 left parenthesis x plus 1 right parenthesis minus 2 greater than minus 4 left parenthesis x minus 4 right parenthesis plus 24(x+1)−2>−4(x−4)+2
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Part 1
Select the correct choice and fill in the answer box to complete your choice.
A.
xgreater than>enter your response here
B.
xless than or equals≤enter your response here
C.
xgreater than or equals≥enter your response here
D.
xless than<enter your response here

Answer 1

To solve the inequality \( 4(x + 1) - 2 > -4(x - 4) + 24 \), let's simplify both sides step-by-step.

1. Expand both sides of the inequality:

   Left side: \[ 4(x + 1) - 2 = 4x + 4 - 2 = 4x + 2 \]

   Right side: \[ -4(x - 4) + 24 = -4x + 16 + 24 = -4x + 40 \]

2. Set up the inequality:

   Now we can rewrite the inequality: \[ 4x + 2 > -4x + 40 \]

3. Add \( 4x \) to both sides:

   \[ 4x + 4x + 2 > 40 \] \[ 8x + 2 > 40 \]

4. Subtract 2 from both sides:

   \[ 8x > 40 - 2 \] \[ 8x > 38 \]

5. Divide both sides by 8:

   \[ x > \frac{38}{8} \] \[ x > 4.75 \]

Now, we can summarize our solution:

Part 1: The solution is \( x > 4.75 \).

Part 2: Graph the solution

On a number line, you would mark a point at \( 4.75 \) with an open circle to indicate that \( 4.75 \) is not included in the solution. Then shade to the right of \( 4.75 \) to show all values greater than \( 4.75 \).

Select the correct choice: A. \( x > 4.75 \)

This is the answer.