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2.5: Solving Equations with a Variable on Each Side
Ex. 1: Solve the following equations. Check your solutions.
1.) 2(2x + 4) = 16
2.) – 3(3x – 4) + 2x = 21 – 7
3.) 4(x – 3) + 3x – 7 = 2
4.) 2(4x – 3) – 3(x + 4) = 4
How to Solve Equations with a variable on both sides:
Steps:
1. Use the ______________________
to remove grouping symbols.
2. ___________ the expressions on each side of the equals sign
3. Use subtraction/ addition to get the _________ on the ____side
of the equal sign and the _________________________ on the
________side.
4. Combine _______________ (simplify) on each side
5. Isolate the ______________ to solve
a. If the solution results in a ________ statement, there is _____ solution:
b. If the solution results in an __________, the solution is ______ numbers
Ex. 2: Simplify the expressions
5.) -2 + 10p = 8p – 1
1
7.) 4(2r  8)  (49r  70)
7

6.) 2x + 4 = 6x – 12
8.) 2(3x – 8) = 10x + 4
Ex. 3: Special scenario. Solve the following equations. Check your solutions.
9.) 7 – 3r = r – 4(2 + r)
10.) 5h – 7 = 5(h – 2) + 3
11.) 2m + 5 = 5(m – 7) – 3m
12.) 3(k + 1) – 5 = 3k – 2