Question

what are the solutions for \\(\frac{1}{5}x + 7 \leq 11\\) and \\(-\frac{1}{5}x - 7 \geq -11\\)?

Explanation:

Step1: Solve the first inequality $\frac{1}{5}x + 7 \leq 11$

Subtract 7 from both sides: $\frac{1}{5}x + 7 - 7 \leq 11 - 7$
Simplify: $\frac{1}{5}x \leq 4$
Multiply both sides by 5: $\frac{1}{5}x \times 5 \leq 4 \times 5$
Simplify: $x \leq 20$

Step2: Solve the second inequality $-\frac{1}{5}x - 7 \geq -11$

Add 7 to both sides: $-\frac{1}{5}x - 7 + 7 \geq -11 + 7$
Simplify: $-\frac{1}{5}x \geq -4$
Multiply both sides by -5 (and reverse the inequality sign): $-\frac{1}{5}x \times (-5) \leq -4 \times (-5)$
Simplify: $x \leq 20$

Answer:

$x \leq 20$