Question

solve for x and graph the solution on the number line below.
-x + 3 ≤ -3 and -x + 3 > -8
answer attempt 1 out of 2
inequality notation:
number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12

Explanation:

Step1: Solve \(-x + 3 \leq -3\)

Subtract 3 from both sides: \(-x \leq -3 - 3\)
Simplify: \(-x \leq -6\)
Multiply both sides by -1 (reverse inequality): \(x \geq 6\)

Step2: Solve \(-x + 3 > -8\)

Subtract 3 from both sides: \(-x > -8 - 3\)
Simplify: \(-x > -11\)
Multiply both sides by -1 (reverse inequality): \(x < 11\)

Step3: Combine the inequalities

From Step1 and Step2, we have \(x \geq 6\) and \(x < 11\), so the solution is \(6 \leq x < 11\)

Answer:

Inequality Notation: \(6 \leq x < 11\)
(For the number line: Plot a closed circle at 6 and an open circle at 11, then shade the region between them.)