Help! I don't get this.
solve each inequality. Graph the solution set, if there is one.
1. n-4>11
2. 4q<12
3. 2v+1>7
4. a+3<11
5. 36<x/-9
6. -y/2>4
7. -6>s/3
8. x/2-4>-6
Please note the correct spelling of this subject: Algebra
To solve each inequality and graph the solution set, we need to follow a few steps:
1. Isolate the variable on one side of the inequality symbol (<, >, ≤, ≥).
2. Solve the inequality by performing the appropriate operations.
3. Graph the solution set on a number line.
Let's go through each problem one by one:
1. n - 4 > 11:
- Add 4 to both sides to isolate the variable: n > 15.
- Graph the solution set by placing an open circle on 15 and shading to the right.
2. 4q < 12:
- Divide both sides by 4 to isolate the variable: q < 3.
- Graph the solution set by placing an open circle on 3 and shading to the left.
3. 2v + 1 > 7:
- Subtract 1 from both sides to isolate the variable: 2v > 6.
- Divide both sides by 2 to solve the inequality: v > 3.
- Graph the solution set by placing an open circle on 3 and shading to the right.
4. a + 3 < 11:
- Subtract 3 from both sides to isolate the variable: a < 8.
- Graph the solution set by placing an open circle on 8 and shading to the left.
5. 36 < x / -9:
- Multiply both sides by -9 (remember that when dividing or multiplying by a negative number, the inequality sign flips): -9 * 36 > x.
- Solve the inequality: -324 > x.
- Graph the solution set by placing an open circle on -324 and shading to the left.
6. -y / 2 > 4:
- Multiply both sides by 2 (remember that when multiplying or dividing by a negative number, the inequality sign flips): -2y > 8.
- Divide both sides by -2 to solve the inequality: y < -4.
- Graph the solution set by placing an open circle on -4 and shading to the left.
7. -6 > s / 3:
- Multiply both sides by 3 (remember that when multiplying or dividing by a negative number, the inequality sign flips): -18 > s.
- Graph the solution set by placing an open circle on -18 and shading to the left.
8. x / 2 - 4 > -6:
- Add 4 to both sides to isolate the variable: x / 2 > -2.
- Multiply both sides by 2 to solve the inequality: x > -4.
- Graph the solution set by placing an open circle on -4 and shading to the right.
Remember to carefully follow these steps for each inequality to find the correct solution set.