Algebraic Equations Study Guide: GED Math (page 3)

Practice problems for these concepts can be found at:

Algebra and Functions Practice Problems: GED Math

Equations

An algebraic equation is a math sentence. It always has an equal (=) sign. Algebraic equations say one quantity is equal to another quantity. Here are a few examples of algebraic equations:

An equation is solved by finding a number that is equal to an unknown variable. To solve for the value of the variable, you first need to get it alone on one side of the equal sign. This is sometimes called isolating the variable.

You want to get the variable alone on one side of the equal sign, so you perform mathematical operations to both sides of the equation to isolate the variable. With every step you take to solve the equation, you should ask yourself, "What operations can I use to get the x alone on one side of the equal sign?" But remember, whatever you do to one side of the equation, you have to do to the other.

Examples

1. Solve the following algebraic equation: x + 5 = 10.

What operation is used in the equation? Addition. In order to get the x alone, you will need to get rid of the 5. So, you should use the inverse operation and subtract. Remember, you have to perform the operation to both sides of the equation:

Combine like terms on both sides of the equal sign:

Therefore, x = 5.

You can check your answer by going back to the original equation and plugging in your answer for x. If your answer makes the algebraic equation true, then it's correct. Let's try it out: x + 5 = 10, and x = 5, so 5 + 5 = 10.

You know that 10 = 10, so your answer, x = 5, is correct.

2. Solve the following algebraic equation: z – 3 = 8.

Ask yourself: What operation is used in the equation? Subtraction. What is the inverse operation of subtraction? Addition. So, add 3 to each side of the equation in order to isolate the variable:

Combine like terms on both sides of the equal sign:

Therefore, z = 11.

Again, check your answer by going back to the original equation and plugging in your answer: z – 3 = 8, and z = 11, so 11 – 3 = 8. You know that 8 = 8, so your answer, z = 11, is correct.

3. Solve the following algebraic equation: 5r = –25.

Ask yourself: What operation is used in the equation? Multiplication. What is the inverse operation of this multiplication? Division. So, divide each side of the equation by 5 in order to isolate the variable: .

Combine like terms on both sides of the equal sign: and .

So, r = –5.

4. Solve the following algebraic equation: = 12.

What operation is used in the equation? Division. What is the inverse operation of this division? Multiplication. So, multiply each side of the equation by 2 in order to isolate the variable.

2 × () = 12 × 2

Combine like terms on both sides of the equal sign: = x and 12 × 2 = 24.

Therefore, x = 24.