Question

1. $6 - xleq5 + 2x<17x$

Explanation:

Step1: Split the compound - inequality

Split $6 - x\leq5 + 2x<17x$ into two inequalities: $6 - x\leq5 + 2x$ and $5 + 2x<17x$.

Step2: Solve the first inequality

Solve $6 - x\leq5 + 2x$.
Add $x$ to both sides: $6\leq5 + 3x$.
Subtract 5 from both sides: $1\leq3x$.
Divide both sides by 3: $\frac{1}{3}\leq x$.

Step3: Solve the second inequality

Solve $5 + 2x<17x$.
Subtract $2x$ from both sides: $5 < 15x$.
Divide both sides by 15: $\frac{1}{3}

Answer:

$x>\frac{1}{3}$