# Intro to equations

Learn what an equation is and what it means to find the solution of an equation.

# What is an equation?

An equation is a statement that two expressions are equal. For example, the expression 5, plus, 3 is equal to the expression 6, plus, 2 (because they both equal 8), so we can write the following equation:
5, plus, 3, equals, 6, plus, 2
Here are two more examples of equations:
6, minus, 2, equals, 3, plus, 1
7, minus, 4, equals, 3
Let's make sure we know the difference between an expression and an equation.
Which of these is an equation?

# True equations

All of the equations we just looked at were true equations because the expression on the left-hand side was equal to the expression on the right-hand side. Let's make sure we understand what a true equation is.
Which of these are true equations?

# Solutions to algebraic equations

All of the equations that we've looked at so far have included only numbers, but most equations include a variable. For example, the equation x, plus, 2, equals, 6 has a variable in it. Whenever we have an equation like this with a variable, we call it an algebraic equation.
For an algebraic equation, our goal is usually to figure out what value of the variable will make a true equation.
For the equation x, plus, 2, equals, 6, notice how start color blueD, x, equals, 4, end color blueD creates a true equation and start color redD, x, equals, 3, end color redD creates a false equation.
True equationFalse equation
space \begin{aligned} \blueD x +2 &= 6 \\\blueD{4} +2 &\stackrel{\large?}{=} 6\\6 &= 6 \end{aligned}space \begin{aligned} \redD x +2 &= 6\\\redD{3} +2 &\stackrel{\large?}{=} 6\\5 &\neq 6 \end{aligned}
Notice how we use the symbol $\stackrel{\large?}{=}$ when we're not sure if we have a true equation or a false equation.
The value of the variable that makes a true equation is called a solution to the equation. Going back to our example, start color blueD, x, equals, 4, end color blueD is a solution of x, plus, 2, equals, 6 because it makes the equation true.

# Let's try a few problems

### Problem 1

Select the solution to the equation.
3, plus, g, equals, 10

### Let's plug in $g=\redD{6}$g, equals, start color redD, 6, end color redD and see if the equation is true.

space \begin{aligned} 3+g &= 10 \\ 3+\redD{6} &\stackrel{\large?}{=} 10\\ 9 &\neq 10 \end{aligned}
No, g, equals, start color redD, 6, end color redD is not the solution.

### Let's try $g = \blueD{7}$g, equals, start color blueD, 7, end color blueD.

space \begin{aligned} 3+g &= 10 \\ 3+\blueD{7} &\stackrel{\large?}{=} 10\\ 10 &= 10 \end{aligned}
Yes, g, equals, start color blueD, 7, end color blueD is the solution!

g, equals, start color blueD, 7, end color blueD is the solution.

### Problem 2

Select the solution to the equation.
3, equals, k, minus, 2

### Problem 3

Select the solution to the equation.
10, equals, 2, w