Solving Equations Like Terms and Variables on Both Sides

5n + 34 = -2 (1 - 7n)

• n = 4

• n = -4

• n = 23/34

• n = 36/19

2(4x - 3) - 8 = 4 + 2x

• x = 1

• x = 3

• x = 5/6

• x = -3

24a = -4(10 - a)

• a = -2

• a = 2

• a = 7/10

• a = -7/10

What should you do first when solving equations?

• Eliminate the parentheses

• Combine like terms

• Isolate the variable

• Whatever you do to one side do to the other.

Like terms must have _____________________________________ and _________________________.

• same variable and same power or exponent

• same variable and number

• exponent and number

• same variable and the same sign

What has to be done BEFORE you start solving a basic two-step equation?

• distributive property, combining like terms, and getting the variables all on one side

• distibutive property, move the variables to one side, cimbine like terms

• distributive property, cancel the constants, get variables to one side

• distributive property, combine like terms, eliminate the constant

2x +7 = -8x - 9 +10x

• no solution

• identity

• one solution

• infinitely many

3 - 7t = -5t + 3 - 2t

• infinitely many

• no solution

• one solution

• t = 8

-6a -15 = -3(a - 7)

• one solution

• no solution

• infinitely many

• a = 12

So how do you know when it is "infinitely many" solutions?

• The constants are the same on both sides of the equal sign.

• The constants are the different on both sides of the equal sign.

• The variables are the same w/ different constants.

• The variables are the same w/ same constants.