Algebra Equations – How to Solve Them

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Algebra. The word may strike fear in the hearts of some who read this, but we promise, solving algebra math equations isn’t as hard as it sounds! This tutorial will show you how to solve algebraic equations, complete with equation examples and their solutions.

You might wonder, “when will I ever need to solve even simple algebra equations in real life?” Math in general and algebra specifically come in handy if you plan to become a:

  • Scientist
  • Teacher
  • Computer Programmer
  • Doctor
  • Statistician

Solving basic algebra equations prepares your brain for handling other difficult tasks, like learning how to code or taking up a musical instrument. Most careers in technology will require an understanding of algebra math equations.

What Is an Algebra Equation?

Before we get into some algebra equations examples, let’s talk about algebra. Algebra is a lot like arithmetic with a mystery element. You still have the same basic symbols:

  • Division: ÷
  • Addition: +
  • Multiplication: ×
  • Subtraction: –

But to find an algebra solution, you have to find a number that’s hidden behind a letter, usually “x.”

Let’s go over some essential algebra terms:

Variable

The letter hiding the solution, commonly “x.”

Constant

Known numbers in the equation. In the equation 2+3=x, 2 and 3 are the constants.

Equation

The chunk of math that needs solving. Equation examples would be “4x+3=11” and “9÷x=3.”

Expression

Numbers and symbols on one side of an equation. “4x+3” and “9÷x” are expressions.

Term

Parts of the expression separated by a math symbols sign. In the previous example of “4x+3,” “4x,” and “3” are both terms.

Coefficient

The numerical part of the term is the coefficient, including the plus or minus sign in front of it. For “4x+3=11,” “4x” would have a coefficient of “4.” If the equation were “3-4x=11,” the coefficient would be “-4.”

Let’s compare algebra math equations with arithmetic equations. A normal arithmetic equation may look something like this:

2+2=

An algebra equation would look like this:

2+2=x

We have the letter “x” where the mystery number will be when we find the algebra solution. Because we know that 2 and 2 make 4, we can now solve for “x.”

Why would anyone bother with algebra when simple algebra equations are nearly identical to arithmetic problems?

Algebra math equations allow for far more complexity than standard arithmetic. This kind of problem-solving is essential for kids learning STEM topics. Let’s look at some more algebra equations examples with answers.

In the following equation, we’ve moved “x” to the other side of the equal sign:

x+9=15

Basic algebra math equations like this are easier to perform without a calculator or a piece of paper. To arrive at the solution, we want to translate the equation into a more easily understood form.

We know we have to add a number to 9 to get to 15, so we could rewrite the equation this way:

15-9=x

Changing the order of the expression makes the algebra solution apparent. Punch the equation into a calculator, and you’ll get your answer:

15-9=6

So now we know that:

x=6

How to Solve Algebra Equations

[Picture of a chalkboard with basic algebra problem]

So far, we’ve done fairly simple algebra math equations, but let’s come up with some harder algebra math equations examples.

Let’s add in some multiplication and division!

(8×2)÷x=4

The parentheses indicate we need to multiply 8 and 2 before we divide by “x.”

Unlike in previous algebra math equations examples, we want to perform some of the math in the problem first:

16÷x=4

We can then rewrite the equation to be simpler to read:

x×4=16

Because 16 divided by the mystery number equals 4, we know that 4 times the mystery number must equal 16. To find x, we can “balance the equation.” In other words, anything we do on one side of the equals sign is something we can do on the other:

(x×4) ÷ 4 = 16 ÷ 4

We can divide both sides by 4 to arrive at “x”:

x=16÷4

x=4

And now you know!

Phina Pipia

Phina Pipia is a writer, educator, and performer. Her work can be found at phinapipia.com.

Phina Pipia

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