Question

Solve, write your answer using interval notation when possible.

1) 5 - a > 0
2) 4(3x + 2) + 6 ≥ 7x - 9

Answer 1

To solve the inequalities, you need to isolate the variable by performing inverse operations. For the first inequality, you subtract 5 and reverse the inequality sign. For the second inequality, you simplify and divide both sides by 5, noting to reverse the inequality sign.

Step-by-step explanation:

1) 5 - a > 0:

1. Subtract 5 from both sides: -a > -5
2. Divide both sides by -1 (remember to reverse the inequality sign): a < 5

The solution in interval notation is (-∞, 5).

2) 4(3x + 2) + 6 ≥ 7x - 9:

1. Distribute 4 into the parentheses: 12x + 8 + 6 ≥ 7x - 9
2. Combine like terms: 12x + 14 ≥ 7x - 9
3. Subtract 7x from both sides: 5x + 14 ≥ -9
4. Subtract 14 from both sides: 5x ≥ -23
5. Divide both sides by 5: x ≥ -23/5

The solution in interval notation is [-23/5, +∞).