Questions: Solve and graph. -4 < 6 - 2x ≤ 8 The solution set in interval notation is □ (Simplify your answer. Type integers or fractions.)

$Solve and graph. -4 < 6 - 2x ≤ 8 The solution set in interval notation is □ (Simplify your answer. Type integers or fractions.)$

Transcript text: Solve and graph. \[ -4<6-2 x \leq 8 \] The solution set in interval notation is $\square$ (Simplify your answer. Type integers or fractions.)

Solution

Solution Steps

Step 1: Isolate the inequality

Start with the given inequality: \[ -4 < 6 - 2x \leq 8 \]

Step 2: Subtract 6 from all parts

Subtract 6 from all parts of the inequality to isolate the term containing $ x $: \[ -4 - 6 < -2x \leq 8 - 6 \] \[ -10 < -2x \leq 2 \]

Step 3: Divide by -2 and reverse the inequality signs

Divide all parts of the inequality by $-2$. Remember to reverse the inequality signs when dividing by a negative number: \[ \frac{-10}{-2} > x \geq \frac{2}{-2} \] \[ 5 > x \geq -1 \]

Step 4: Rewrite the inequality in standard form

Rewrite the inequality in the standard form (from smallest to largest): \[ -1 \leq x < 5 \]

Step 5: Write the solution in interval notation

The solution set in interval notation is: \[ [-1, 5) \]