Question

Peyton is altering her new jacket to enter it into the Bodacious Bedazzling Contest. In order for a garment to be considered "bedazzled," it must contain an amount of gems that fall within the range of the following inequality 132 ≤ ½x + 8 ≤ 193. Find the range of gems Peyton must use to enter he jacket in the contest.

Answer 1

248 to 370 gems
set up two equations
132=(1/2)x+8 x=248
193=(1/2)x+8 x=370

Answer 2

the range will be 248 ≤ x ≤ 370

Explanation:

The given inequality models the range of amount of gems.

132 ≤ 1/2x + 8 ≤ 193

So we have to solve the inequality for the value of x.

132 ≤
`(1)/(2)x` + 8 ≤ 193

Now we subtract 8 from the inequality.

132 - 8 ≤ (
`(1)/(2)x` + 8) - 8 ≤ 193 - 8

124 ≤
`(x)/(2)` ≤ 185

Now we multiply the inequality by 2

124 × 2 ≤
`((x)/(2))` × 2 ≤ 185 × 2

248 ≤ x ≤ 370

So the range will be 248 ≤ x ≤ 370