Solving Equations

Solving algebra equations is difficult for many. If you struggle with algebra solving equations can be improved using this lesson and practice.

Checking your work

It's important to check your work in algebra, especially when you're first getting started. Luckily, checking your work when you're simplifying equations is pretty straightforward. All you have to do is replace the variable in the equation with the value you found when you simplified it. To see how this works, let's look back at one of the equations we simplified before:

4 (3y - 8) = 4

We found that y was equal to 3. Let's see if we got the answer right.

Here's our original equation. y is our variable, so we'll be replacing it with the value we found: 3.

4 (3y - 8) = 4

Here's what the equation looks like with 3 instead of y. Now we're going to see if the equation is true. If the left side is equal to the right side, our answer is correct.

4 (3 ⋅ 3 - 8) = 4

We'll follow the order of operations, with parentheses first. 3 ⋅ 3 is 9, and 9 - 8 is 1.

4 (1) = 4

Now that we've simplified the parentheses, all we have to do is multiply 4 times 1.

4 (1) = 4

4 ⋅ 1 is 4. Both sides of our equation are equal, so our answer is correct!

4 = 4

That's all it takes! Checking every expression you simplify is a good habit to get into, and you'll find that checking your work usually takes less time than it took to simplify the equation in the first place.

Let's try one more:

The expression we'll be looking at is 5x + 3 = 23 + x. We're checking to see if the solution x = 4 is correct.

5x + 3 = 23 + x

First, we'll replace the variable x with 4.

5 ⋅ 4 + 3 = 23 + 4

To check our work, we'll have to simplify both sides of the expression. We'll start with the left side. According to the order of operations, we need to multiply first, then add. 5 ⋅ 4 is 20, and when you add 3 to that, you get 23.

5 ⋅ 4 + 3 = 23 + 4

Now we need to simplify the right side: 23 + 4 is 27.

23 = 23 + 4

Our equation can't be right—23 and 27 are not equal. We now know that x does not equal 4. In other words, the answer is incorrect.

23 = 27

As you just saw, if you're checking a problem and the final expression is not a balanced equation, your answer is not correct. Take time to go back and simplify your original equation again. On your second try, pay careful attention to the order of operations, and make sure you're adding, subtracting, multiplying, and dividing correctly.

Want to check that last problem again? This time, check it with x = 5.

Practice!

Problem 1

Check this problem. Is u = 6 the correct answer? If not, what is?

u (3 + 8) / 2 = 33

Problem 2

Check this problem. Is v = 5 the correct answer? If not, what is?

v / 5 + 20v = 19v + 12

Problem 3

Check this problem. Is w = 8 the correct answer? If not, what is?

5w + 3 = 4w + 10

Answers

  1. Yes, the answer is correct.
  2. No; v = 10.
  3. No; w = 7.

Assessment

Want even more practice? Try out a short assessment to test your skills by clicking the link below:

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