Tips for solving equations

All equations have an equal sign. This symbol comes from the Greek word prefix equa which translates into balance so both the left hand member AND the right hand member of the equation have the same value. Our goal is to find the missing part, usually represented by a letter (variable).

Treat any equation as if the equal sign was the perfect balance point of a teeter-totter. Remember, if you do anything to the left hand member you MUST do the same thing to the right hand member in order to keep the values exactly the same ON BOTH SIDES!

Problem: Solve: x – 4 = 13

Solution: In order to get the variable x all by itself, you have to eliminate the – 4 FROM BOTH SIDES! The way to do this is to make a number that is the OPPOSITE of – 4. Use + 4 as the OPPOSITE of – 4 and arrange it in your problem ON BOTH SIDES of the equal sign so it is under LIKE TERMS.

x – 4  =  13

   + 4_  + 4 BOTH SIDES

x        =  17 answer

In some problems, you will see variables on both sides of the equation. Your goal is to get one variable on one of the sides all by itself in order to solve the problem.

Problem: Solve: 5x – 6 = – 3x + 10

Solution: I suggest you attempt to move the SMALLEST variable to the other side of the equation whenever possible as it seems to keep the variables positive most of the time. In this problem – 3x is smaller than 5x so we will take the OPPOSITE if – 3x, which is + 3x and write it ON BOTH SIDES of the equation and place it under LIKE TERMS.

5x – 6 = – 3x + 10

3x _ ­­       _3x ____ BOTH SIDES

2x = 10

2       2

x = 5 answer

More advanced problem: Solve: 3(4y – 10) + 2(–2y + 7) = –2(–3y – 6)

Solution: You have to use the distributive property to eliminate the parenthesis before working with combining LIKE TERMS.

3(4y – 10) + 2(–2y + 7) = –2(–3y – 6)

12y – 30 – 4y + 14 = 6y + 12

Combine LIKE TERMS:

8y – 16 = 6y + 12

Take the OPPOSITE of 6y (the smallest of the letters), which is – 6y, and write it ON BOTH SIDES of the equation lining up LIKE TERMS:

   8y – 16 = 6y + 12

– 6y         – 6y____ BOTH SIDES

2y – 16    =         12

      +16            +16

2y        =           28

2                        2

y = 14 answer