Question

Which solutions do the inequalities 1/2(5r+3) is greater than or equal to 14 and -2s+6 is vreater than or equal to -8

Answer 1

The solutions to the inequalities 1/2(5r+3) ≥ 14 and -2s+6 ≥ -8 are r ≥ 5 and s ≤ 7, respectively, after isolating the variables and simplifying the expressions.

Step-by-step explanation:

The student asked for the solution to two inequalities: 1/2(5r+3) ≥ 14 and -2s+6 ≥ -8.

To solve these, we need to isolate the variable (r or s) on one side of the inequality.

For the first inequality:

1. Multiply both sides by 2 to get rid of the fraction: 5r + 3 ≥ 28.
2. Subtract 3 from both sides: 5r ≥ 25.
3. Divide both sides by 5: r ≥ 5.

For the second inequality:

1. Add 2s to both sides: 6 ≥ 2s - 8.
2. Add 8 to both sides: 14 ≥ 2s.
3. Divide both sides by 2: s ≤ 7.

The solutions to the inequalities are r ≥ 5 and s ≤ 7.