Question

A.)List the 4 steps outlined in the lesson on solving equations. (1 points)

B.)Solve each equation and show all work (3 points each)

1.) 5x + 7 = 3x + 21

2.) 3x - 2(5 - x) = -3(x - 10) + 3x

3.) 5(x + 1) = 3(2x + 3) + 5

Answer 1

For this case we must solve the following equations:

`5x + 7 = 3x + 21`

We subtract 3x on both sides of the equation:

`5x-3x + 7 = 21`

We subtract 7 on both sides of the equation:

`5x-3x + 21-72x = 14`

We divide between 2 on both sides of the equation:

`x = \frac {14} {2}\\x = 7`

The second equation is:

`3x-2 (5-x) = - 3 (x-10) + 3x`

We apply distributive property to the terms of parentheses:

`3x-10 + 2x = -3x + 30 + 3x`

We add common terms:

`5x-10 = 30`

We add 10 to both sides of the equation:

`5x = 30 + 10\\5x = 40`

We divide between 5 on both sides of the equation:

`x = \frac {40} {5}\\x = 8`

Third equation:

`5 (x + 1) = 3 (2x + 3) +5`

We apply distributive property to the terms within parentheses:

`5x + 5 = 6x + 9 + 5`

We add similar terms:

`5x + 5 = 6x + 14`

We subtract 6x on both sides of the equation:

`5x-6x + 5 = 14`

We subtract 5 on both sides of the equation:

`-x = 14-5\\-x = 9\\x = -9`

Answer:

`x = 7\\x = 8\\x = -9`