50 pts!!! Given: x - 6 1/3 ≤ 1 1/2. Choose the solution set. A.x B.x C. x R, x ≤ 5

Question

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

A.x

B. x R, x ≤ 7

C.x

Answer 1

x

Explanation:

we have

`x-6(1)/(3) \leq 1(1)/(2)`

Convert mixed number to an improper fraction first

`6(1)/(3)=(6*3+1)/(3)=(19)/(3)`

`1(1)/(2)=(1*2+1)/(2)=(3)/(2)`

substitute

`x-(19)/(3) \leq (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 (47)/(6)`

convert to mixed number

`(47)/(6)=(42)/(6)+(5)/(6)=7(5)/(6)`

substitute

`x\leq 7(5)/(6)`

therefore

x R, x ≤ 7 5/6