Question

PLEASE HELP!!!!!

1. Determine the number of solutions for the equation 1 - 3(x - 2) = 7 - 3x
A. infinite solutions
B. no solutions
C. one solution

2. Solve the following and show all work.

The length of a rectangle is 4 less than 3 times the width. If the perimeter is 40, find the dimensions of the rectangle.


3. Solve the following and show all work.

Jim is 5 years older than Cindy. 4 years ago, the sum of their ages was 21. Find each of their ages now.

4. Solve the inequality below and select the best explanation of its graph. -8+7r>10r-23

A. Open circle on 2 and line pointing to the left.
B. Open circle on 5 and line pointing to the left.
C. This is an incorrect answer. Have a nice day!
D. Open cirle on 5 and line pointing to the right.

5. Use an inequality to solve the following problem. Show all work.

Rita plans to spend at most $115.00 on a skirt and two blouses. She bought the two blouses for $38.95 each. How much can she spend on the skirt?

Answer 1

Let x = the width

it says, "The length of a rectangle is 4 less than 3 times the width." write that as:
L = 3x - 4

If the perimeter is 40, find the dimensions of the rectangle.

We know: 2L + 2W = 40

Substitute (3x-4) for L and x for W
2(3x-4) + 2x = 40

6x - 8 + 2x = 40; multiplied what's inside the brackets

6x + 2x = 40 + 8; do some basic alegbra to find x; (added 8 to both sides)

8x = 48

x = 48/8

x = 6 which is the width

It said that L = 3x - 4, therefore:
L = 3(6) - 4
L = 18 - 4
L = 14; is the length

Check our solutions in the perimeter:
2(14) + 2(6) =
28 + 12 = 40