Question

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

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:

$x = 7\\x = 8\\x = -9$