Question

Solve the equation for y: 4(2y-6)+3=11

Answer 1

Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {1, 2, 3, 4}. What is P'?

Answer 2

Solve the inequality: 4x-3>21

Answer 3

Your goal is to save at least $360.00 over the next 6 weeks. How much money must you save each week to meet that goal? Write and solve an inequality.

Answer 4

We start by distributing 4 to 2y and -6:
8y - 24 + 3 = 11
Next, we combine like terms:
8y - 21 = 11
Next, we add 21 to both sides of the equation to isolate the variable term:
8y = 32
Lastly, we divide both sides of the equation by 8:
y = 4

Answer 5

P' is the complement of set P in the universal set U. It contains all the elements in U that are not in P.

In this case, the universal set U = {1, 2, 3, 4, 5, 6, 7, 8} and set P = {1, 2, 3, 4}.

To find P', we need to find the elements in U that are not in P.

P' = {5, 6, 7, 8}

Answer 6

To solve the inequality, we need to isolate the variable x.

We start by adding 3 to both sides of the inequality to get rid of the constant term -3:

4x - 3 + 3 > 21 + 3

This simplifies to:

4x > 24

Next, we divide both sides of the inequality by 4 to isolate the variable x:

(4x)/4 > 24/4

This simplifies to:

x > 6

So the solution to the inequality is x > 6.

Answer 7

To solve this problem, let's assume x represents the amount of money that needs to be saved each week.

From the problem, we know that the total amount of money saved over the 6 weeks should be at least $360.00. Therefore, we can set up the following inequality:

6x ≥ 360

To solve for x, we need to isolate the variable. We can do this by dividing both sides of the inequality by 6:

(6x)/6 ≥ 360/6

This simplifies to:

x ≥ 60

So, in order to meet the goal of saving at least $360.00 over the next 6 weeks, you must save at least $60.00 each week.