Heather's age is 3 years more than half her cousin rachel's age. if the difference in their ages is less than 4 years, what is the oldest that rachel can be in years?

: H = Heather's age R = Rachel's age first sentence: H = R/2 + 3 second: |H - R| ≤ 4 Sub for H: |R/2 + 3 - R| = |3 - R/2| ≤ 4 At the endpoints we have 3 - R/2 = 4 which doesn't have a positive solution 3 - R/2 = -4 → R/2 = 7 → R = 14 Check: H = (14/2) + 3 = 10 √ Rachel must be an even number of years old (we divide her age by 2).

Use the variable h as Heather's age and r as Rachel's age.
Equation:
h= 3 + 1/2r
Multiplication property of equality:
2x = 3+r
Simplify:
2x - r = 3
x - r < 4
x-2x +3 < 4

x < -1