14. Solve the inquality -3(r-11) + 15 equal or greater than 9.
15.Solve the inequality: -2 < 4z = 10 lessthan or equal to 12.
16. Solve the inequality 2x-5 less than or equal to 10 or 33 - 4x < 5
17. Solve the inequality 3 | m -4 | > 6
Step 14:
To solve the inequality -3(r-11) + 15 ≥ 9, follow these steps:
Step 1: Distribute the -3 to the terms inside the parentheses:
-3r + 33 + 15 ≥ 9
Step 2: Combine like terms:
-3r + 48 ≥ 9
Step 3: Subtract 48 from both sides of the inequality:
-3r ≥ -39
Step 4: Divide both sides of the inequality by -3. Since we are dividing by a negative number, the direction of the inequality symbol will change:
r ≤ 13
So, the solution to the inequality is r ≤ 13.
Step 15:
To solve the inequality -2 < 4z ≤ 10, follow these steps:
Step 1: Split the inequality into two separate inequalities:
-2 < 4z and 4z ≤ 10
Step 2: Solve each inequality separately:
For the first inequality, -2 < 4z:
Divide both sides by 4 to isolate z:
-2/4 < z
-1/2 < z
For the second inequality, 4z ≤ 10:
Divide both sides by 4 to isolate z:
4z/4 ≤ 10/4
z ≤ 5/2
Step 3: Combine the solutions:
-1/2 < z ≤ 5/2
So, the solution to the inequality is -1/2 < z ≤ 5/2.
Step 16:
To solve the inequality 2x - 5 ≤ 10 or 33 - 4x < 5, follow these steps:
Step 1: Solve the first inequality, 2x - 5 ≤ 10:
Add 5 to both sides of the inequality:
2x ≤ 15
Divide both sides by 2 to isolate x:
x ≤ 15/2
Step 2: Solve the second inequality, 33 - 4x < 5:
Subtract 33 from both sides of the inequality:
-4x < 5 - 33
-4x < -28
Divide both sides by -4. Since we are dividing by a negative number, the direction of the inequality symbol will change:
x > -28/(-4)
x > 7
Step 3: Combine the solutions:
x ≤ 15/2 or x > 7
So, the solution to the inequality is x ≤ 15/2 or x > 7.
Step 17:
To solve the inequality 3 | m - 4 | > 6, follow these steps:
Step 1: Break the inequality into two separate inequalities:
3 (m - 4) > 6 and -(m - 4) > 6
Step 2: Solve the first inequality, 3 (m - 4) > 6:
Distribute the 3 to the terms inside the parentheses:
3m - 12 > 6
Add 12 to both sides of the inequality:
3m > 18
Divide both sides by 3 to isolate m:
m > 6
Step 3: Solve the second inequality, -(m - 4) > 6:
Distribute the -1 to the terms inside the parentheses:
-m + 4 > 6
Subtract 4 from both sides of the inequality:
-m > 2
Since we are multiplying/dividing by a negative number, the direction of the inequality symbol will change. Multiply both sides by -1:
m < -2
Step 4: Combine the solutions:
m < -2 or m > 6
So, the solution to the inequality is m < -2 or m > 6.
To solve inequalities, we need to isolate the variable on one side of the inequality sign. Here's how to solve each of the given inequalities:
14. -3(r-11) + 15 ≥ 9
Step 1: Simplify the equation.
-3r + 33 + 15 ≥ 9
-3r + 48 ≥ 9
Step 2: Move constants to the other side.
-3r ≥ 9 - 48
-3r ≥ -39
Step 3: Divide both sides of the inequality by -3. Remember to flip the inequality sign when dividing by a negative number.
r ≤ -39 / -3
r ≤ 13
So, the solution to the inequality is r ≤ 13.
15. -2 < 4z ≤ 10
Step 1: Divide both sides of the inequality by 4.
-2/4 < z ≤ 10/4
-1/2 < z ≤ 5/2
So, the solution to the inequality is -1/2 < z ≤ 5/2.
16. 2x - 5 ≤ 10 or 33 - 4x < 5
Let's solve each inequality separately:
For 2x - 5 ≤ 10:
Step 1: Add 5 to both sides of the inequality.
2x ≤ 10 + 5
2x ≤ 15
Step 2: Divide both sides of the inequality by 2.
x ≤ 15 / 2
x ≤ 7.5
For 33 - 4x < 5:
Step 1: Subtract 33 from both sides of the inequality.
-4x < 5 - 33
-4x < -28
Step 2: Divide both sides of the inequality by -4. Remember to flip the inequality sign when dividing by a negative number.
x > -28 / -4
x > 7
So, the solution to the inequality is x ≤ 7.5 or x > 7.
17. 3 |m - 4| > 6
Step 1: Divide both sides of the inequality by 3.
| m - 4 | > 6 / 3
| m - 4 | > 2
Step 2: Split the inequality into two cases, one with a positive absolute value and one with a negative absolute value:
m - 4 > 2 or m - 4 < -2
For m - 4 > 2:
Step 3: Add 4 to both sides of the inequality.
m > 2 + 4
m > 6
For m - 4 < -2:
Step 4: Add 4 to both sides of the inequality.
m < -2 + 4
m < 2
So, the solution to the inequality is m > 6 or m < 2.
Solve the inequality −4y + 6 < −14.
A. y > 2
B. y ≤ 5
C. y > 5
D. y < 5