Please explain. ### Solving the Compound InequalitySolve the following inequality:\[ 5|4x - 2| + 4 \leq 9 \]**Explanation:**1. **Start by isolating the absolute value expression:**\[ 5|4x - 2| + 4 \leq 9 \]Subtract 4 from both sides to isolate the absolute value term:\[ 5|4x - 2| \leq 5 \]2. **Divide both sides by 5:**\[ |4x - 2| \leq 1 \]3. **Solve the absolute value inequality:**Given the absolute value inequality \( |A| \leq B \), this translates to:\[ -B \leq A \leq B \]For our inequality \( |4x - 2| \leq 1 \), this translates to:\[ -1 \leq 4x - 2 \leq 1 \]4. **Solve the compound inequality:**First inequality:\[ -1 \leq 4x - 2 \]Add 2 to both sides:\[ 1 \leq 4x \]Divide by 4:\[ \frac{1}{4} \leq x \]Second inequality:\[ 4x - 2 \leq 1 \]Add 2 to both sides:\[ 4x \leq 3 \]Divide by 4:\[ x \leq \frac{3}{4} \]5. **Combine the solutions:**\[ \frac{1}{4} \leq x \leq \frac{3}{4} \]Thus, the solution to the inequality \( 5|4x - 2| + 4 \leq 9 \) is:\[ \frac{1}{4} \leq x \leq \frac{3}{4} \]This interval notation denotes that \( x \) is between \(\frac{1}{4}\) and \(\frac{3}{4}\) inclusive.

Name: Please explain. ### Solving the Compound InequalitySolve the following
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please explain. ### Solving the Compound InequalitySolve the following inequality:\[ 5|4x - 2| + 4 \leq 9 \]**Explanation:**1. **Start by isolating the absolute value expression:**\[ 5|4x - 2| + 4 \leq 9 \]Subtract 4 from both sides to isolate the ab