Question

Using the properties of inequality, justify both steps in solving the inequality 2/5 m - 8 < -2. (2 points)

2/5 m - 8 < -2

2/5 m - 8 + 8 < -2 + 8

5/2(2/5m) < 5/2 (6)

Solve for m (1 point)

Answer 1

1) 2/5 m - 8 < -2
Add 8 to both sides: 2/5 m - 8 + 8 < -2 + 8.
Justification: Addition property of inequalities — adding the same number to both sides preserves the inequality. This gives 2/5 m < 6.

2) Multiply both sides by 5/2: (5/2)(2/5 m) < (5/2)(6).
Justification: Multiplication property of inequalities — multiplying both sides by the same positive number preserves the inequality. (5/2 is the reciprocal of 2/5, so (5/2)(2/5)m = m.) This yields m < 6·5/2 = 15.

Solution: m < 15.