Solving Equations with Variables on

Both SidesLesson 2-4

Many equations contain variables on each side. To

solve these equations, FIRST use addition and

subtraction to write an equivalent equation with all of

the variables on one side.

Traditionally, the variables (letter) are “moved to the

___________________ and the constants (numbers)

are “moved” to the ________________ side of the

equal sign.

left

right

A. 8 + 5s = 7s – 2

_________________________________ subtract “7s” so variables are on the left.

_________________________________ Simplify

___________________________________ Subtract “8” so constants are on the right.

___________________________________ Simplify

___________________________________ Multiply/Divide

___________________________________ Simplify

CHECK:

__________________________________

___________________________________

____________________________________

8 + 5s – 7s = 7s – 7s – 2

8 – 2s = – 2

8 – 8 – 2s = – 2 – 8

– 2s = – 10

s = 5

8 + 5(5) = 7(5) - 2

Substitute the value of the variable for the

variable

8 + 25 35 - 2

33 33

Multiply both sides by the LCD

12 – r = 2r + 3 Simplify using the distributive property.

12 – r – 2r = 2r – 2r + 3 Subtract 2r from each side, this “moves” the variable to the left side of the equation.12 – 3r = 3 -r -2r = -3r

12 – 12 – 3r = 3 – 12 Subtract 12 from each side, this “moves” the constant to the right side of the equation.

– 3r = – 9 Simplify “3 – 12”

Divide each side by -3 (coefficient of r)

r = 3 Simplify

CHECK:

3 – 0.75 1.5 + 0.75

2.25 2.25

Since the two sides are the same, the equation checks.

Practice solving the problems below. Answers are on the last slide of the part 2 notes.

Solving Equations with Grouping Symbols

6 + 4q = 12q - 42

6 + 4q – 12q = 12q – 12q - 42

6 – 8q = - 42

6 – 6 – 8q = – 42 – 6

– 8q = – 48

q = 6

30 = 30

CHECK:

Yes, there is a “typo” in your notes.

18r – 24 = 21r + 3

18r – 24 – 21r = 21r – 21r + 3

– 3r – 24 = 3

– 3r – 24 + 24 = 3 + 24

– 3r = 27

r = – 9

Use the distributive property.

Subtract 21r from each side to eliminate the variables on the right side..Simplify by combining Like Terms (18r and -21r).

Add 24 to each side to eliminate the constants on the left side.

Simplify (add 3 + 24)

Divide each side by -3 (the coefficient of r.)

Simplify

Check:

Practice solving the problems below. Answers are on the last slide of the part 2 notes.

Please check back for part 2 of these notes where we investigate equations that

have no solution or infinitely many solutions.