Questions: Solve the compound inequality. Graph the solution set, and write the solution in interval notation. -8 ≤ -4x + 5 < 9 The solution set in interval notation is .

Solve the compound inequality. Graph the solution set, and write the solution in interval notation. -8 ≤ -4x + 5 < 9 The solution set in interval notation is .
Transcript text: Unit 1 - Section 1.7 Question 9 of 15 ( 1 point) | Question Attempt: 1 of Unlimited Solve the compound inequality. Graph the solution set, and write the solution in interval notation. \[ -8 \leq-4 x+5<9 \] Part 1 of 2 The solution set in interval notation is $\square$ .
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Solution

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Solution Steps

Step 1: Solve the compound inequality

Given the compound inequality: \[ -8 \leq -4x + 5 < 9 \]

First, we solve the left part of the inequality: \[ -8 \leq -4x + 5 \] Subtract 5 from both sides: \[ -13 \leq -4x \] Divide by -4 and reverse the inequality sign: \[ \frac{-13}{-4} \geq x \] \[ \frac{13}{4} \geq x \] \[ x \leq \frac{13}{4} \]

Next, we solve the right part of the inequality: \[ -4x + 5 < 9 \] Subtract 5 from both sides: \[ -4x < 4 \] Divide by -4 and reverse the inequality sign: \[ x > -1 \]

Combining both parts, we get: \[ -1 < x \leq \frac{13}{4} \]

Final Answer

The solution set in interval notation is: \[ (-1, \frac{13}{4}] \]

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