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 algebraic equations examples. 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 problems 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
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!
How to Solve For X in an Equation… and Y, Too?
We can add other letters for even harder algebra math equations, like the kind you’ll run into in high school and college. It’s important to note that in a single equation, a letter can only represent one number. For example:
x+x=4
Several different numbers could add together to make 4. But since both are represented by x in the equation, they would have to be the same number. You couldn’t have x=1 and x=3; they would both have to be 2.
Now that we’ve established this rule, let’s create two new equations:
(5×6)-x=10+y
3x=y
The reason we need two equations when we have multiple variables is that we need to check whether we’ve gotten “x” and “y” correct by plugging them into a second equation.
You’ll notice there’s no multiplication symbol between the 3 and the x. When we have a number next to a variable, it’s assumed that the two figures will be multiplied. The same goes for numbers next to parentheses in algebra math equations.
We now have variables on both sides of the equation, making this problem more difficult than the more basic algebra equations that came before.
First, we’ll multiply 5 times 6 in the first equation:
30-x=10+y
Now we’re getting somewhere. Let’s isolate “y.” Because we know that “y” plus 10 equals the expression 30 minus “x,” we can subtract 10 from both sides:
20-x=y
Here’s the tricky part: Many numbers would create correct answers to this equation, but there are only two numbers that will work for “x” and “y” if we also want to solve the second equation.
20-x=y
3x=y
Now we can combine the two equations because we know the expressions that equal “y.”
20-x=3x
Now, this looks like a complicated equation in and of itself, right? You will run into algebra math equations more difficult than this! First, let’s understand that 20 minus “x” is also 20 plus negative “x”:
20+-x=3x
We’ll then reorder it to isolate “x” a little more:
-x+20=3x
Now we can subtract 3x from both sides:
-4x+20=0
Now add 4x to both sides:
20=4x
Divide by 4:
20÷4=4x÷4
And we get:
5=x
Now we can plug it back into our original equations to solve for y:
(5×6)-5=10+y
3×5=y
We can see that the second equation will give us 15=y, but let’s solve the first equation to make sure:
30-5=10+y
Then:
25=10+y
Subtract 10 from both sides and:
15=y
We’ve done it!
Order of Operations
So far, you might feel like algebra is a whole new language. Just as grammar is important for the structure of sentences, the order of operations in algebra math equations is really important. Let’s take a look at some algebra math equations examples.
The Distributive Property
When looking for the algebra solution, there are multiple paths for arriving at the final answer. Here, we’re going to look at the distributive property. It’s called the distributive property because we’re distributing the first 3 to both the variable and the 5 inside the parentheses:
3(x-5)=3
Results in:
3x-15=3
We’ve multiplied both the x and the 5 by 3, arriving at 3x and 15. Now we can add 15 to both sides:
3x=18
Divide both sides by 3:
3x÷3=18÷3
To get our solution for “x”:
x=6
Dividing For the Solution
Division is also a great way to find solutions in algebra math equations. Instead of distributing the 3, we can divide both sides by 3:
3(x-5)÷3=3÷3
To arrive at:
x-5=1
Then we can add 5 to both sides to get:
x=6
Being able to solve the equation in multiple ways also helps to check your math. If you get different answers depending on which way you solved the equation, that’s a good sign you need to check your process.
As you can see, the order of operations makes a difference in how to solve algebraic equations. But there’s one more scenario we haven’t looked at…
Algebra: Not So Scary After All
With a little patience and practice, as well as getting familiar with some terms, you’ll be in good shape for figuring out how to solve algebraic equations. Of course, this tutorial is just the tip of the algebraic iceberg!
Whether you’re a student going through school or an adult sharpening up your math skills, finding a good teacher is the best way to learn to solve hard algebra equations. You may not have to find algebra solutions to make a great sandwich or replace light bulbs around your house, but the more math you know, the more career opportunities open up for you.
Think about all of the great inventions you use every day. Your phone, your computer, your car, just about everything electronic came from the mind of a scientist or inventor who relies on math to create devices you can’t live without. Want to set the world on fire with the next great invention? Algebra math equations can help you do it!
Did you have a teacher that made algebra even simpler? Comment below; we’d love to hear about it!
Phina Pipia