Question

Solving equations? Only 5 questions :) Thank you!!!

1. Please show steps to solve. 3m - 5 = 7m - 21

2. Please show steps to solve. 4(x-6) = 2(x-3)

3. Please show steps to solve. 2(n-3) + 5 = 3(n-1)

4. Please show steps to solve. One side of a square is 5n inches long. Another side is n + 16 inches long. Write an equation by setting these equal and solving for n. How long is a side of the square?

5. In the class elections, Connie received 53 more votes than Carl. In all, 221 votes were cast for the two candidates. How many votes did each receive?

Once again, I truly appreciate

Answer 1

1. 3m - 5 = 7m - 21
-5 = 4m - 21
16 = 4m
4m = 16
m = 4

2. 4(x - 6) = 2(x - 3)
4x - 24 = 2x - 6
2x - 24 = -6
2x = 18
x = 9

3. 2(n - 3) + 5 = 3(n - 1)
2n - 6 + 5 = 3n - 3
2n - 1 = 3n - 3
-1 = n - 3
2 = n
n = 2

4. A square, by definition, has equal sides. Therefore...

s = 5n; s = n + 16
5n = n + 16
4n = 16
n = 4

Plug in n = 4 for one of the sides to solve for the length of a side.

s = 5n
s = 5(4) = 20
OR
s = n + 16
s = (4) + 16 = 20

The side length is 20 inches.

And finally...

5. You know that the number of votes Connie has is 53 values more than the number of votes Carl has. We also know that the total votes adds up to 221. We can thus conclude that the number of total votes Connie got plus the number of total votes Carl got equals 221. Therefore, if the base number of votes is represented by X, we know that X + (X + 53) = 221

X + (X + 53) = 221
2X + 53 = 221
2X = 168
X = 84

Carl received X number of votes. Therefore, Carl received 84 votes.

Connie received X + 53 number of votes. Therefore, Connie received 137 votes.

This can be affirmed since 84 + 137 = 221, which is the total number of votes cast in the election.