Question

50 pts!!! Given: x - 6 1/3 ≤ 1 1/2. Choose the solution set.

Answer 1

Answer:

{x | x R, x ≤ 7 5/6 }

Step-by-step explanation:

we have

$x-6\frac{1}{3} \leq 1\frac{1}{2}$

Convert mixed number to an improper fraction first

$6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}$

$1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}$

substitute

$x-\frac{19}{3} \leq \frac{3}{2}$

Multiply by 6 both sides to remove the fractions

$6x-38 \leq 9$

Adds 38 both sides

$6x \leq 9+38$

$6x \leq 47$

Divide by 6 both sides

$x\leq \frac{47}{6}$

convert to mixed number

$\frac{47}{6}=\frac{42}{6}+\frac{5}{6}=7\frac{5}{6}$

substitute

$x\leq 7\frac{5}{6}$

therefore

{x | x R, x ≤ 7 5/6 }