(1 point) 2t + 8 ≥ −4(t + 1) t ≥ _____
show your work
First, distribute -4 to t + 1:
2t + 8 ≥ -4t - 4
Next, combine like terms on the right side of the inequality:
6t + 8 ≥ -4
Subtract 8 from both sides:
6t ≥ -12
Finally, divide both sides by 6 to solve for t:
t ≥ -2
To solve the inequality 2t + 8 ≥ -4(t + 1), we can follow these steps:
Step 1: Distribute the -4 on the right side of the equation:
2t + 8 ≥ -4t - 4
Step 2: Combine like terms on both sides of the equation:
2t + 8 ≥ -4t - 4 becomes
2t + 4t + 8 ≥ -4
Step 3: Simplify both sides of the equation:
6t + 8 ≥ -4
Step 4: Subtract 8 from both sides to isolate the variable:
6t + 8 - 8 ≥ -4 - 8 becomes
6t ≥ -12
Step 5: Divide both sides by 6 to solve for t:
6t/6 ≥ -12/6 becomes
t ≥ -2
So the solution to the inequality is t ≥ -2.
To solve the inequality 2t + 8 ≥ -4(t + 1) step-by-step, we can simplify and isolate the variable t. Here's the work:
1. Distribute -4 to (t + 1):
2t + 8 ≥ -4t - 4
2. Combine like terms:
2t + 8 ≥ -4t - 4
3. Move the -4t term to the left side of the inequality:
6t + 8 ≥ -4
4. Subtract 8 from both sides:
6t ≥ -4 - 8
6t ≥ -12
5. Divide both sides by 6 (since the coefficient of t is 6):
t ≥ -12/6
t ≥ -2
So the solution to the inequality 2t + 8 ≥ -4(t + 1) is t ≥ -2.
(1 point)
5a − 2 < 18
a < _____
show your work
To solve the inequality 5a - 2 < 18:
1. Add 2 to both sides of the inequality:
5a - 2 + 2 < 18 + 2
5a < 20
2. Divide both sides by 5:
(5a)/5 < 20/5
a < 4
Therefore, the solution to the inequality is a < 4.
(1 point)
3x ≤ 21
x ≤
show your work
To solve the inequality 3x ≤ 21:
1. Divide both sides of the inequality by 3:
(3x)/3 ≤ 21/3
This simplifies to:
x ≤ 7
Therefore, the solution to the inequality is x ≤ 7.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A painter earns $15 per hour. What is the minimum number of hours he must work to earn at least $200? Write an inequality to represent this situation and solve. Show your work.
Let's break down the problem step by step:
Step 1: Let x represent the number of hours the painter must work.
Step 2: The painter earns $15 per hour. Therefore, the amount he earns can be represented as 15x.
Step 3: We are looking for the minimum number of hours he must work to earn at least $200. So, we can write the inequality as:
15x ≥ 200
Step 4: To solve the inequality, divide both sides by 15:
(15x)/15 ≥ 200/15
Simplifying, we get:
x ≥ 200/15
Step 5: Divide 200 by 15:
x ≥ 13.33
Therefore, the minimum number of hours the painter must work to earn at least $200 is 13.33 hours (rounded up to the nearest whole number, which would be 14 hours).