# Basic Algebra/Solving Equations/Solving Equations with Addition and Subtraction

Solving simple equations like

x+5=10

is a very important topic in beginning algebra. In this section, we will introduce the concept of a variable.

Don't be scared! It's just a number you don't know yet. Solving an equation can be looked at like you are 'filling in the blank'.

For the example above, what number plus 5 makes 10? The answer is probably pretty apparent to you when you are asked the question that way, but it might seem fuzzy when you see the notation like above, even though it means the exact same thing.

## Vocabulary

Variable - An unknown number which is represented by a letter. Common variables are usually the last letters of the alphabet. i.e. x, y, z. Variables do not necessarily have a set value, as in an expression, x+5 can mean any number plus 5. Only when you have an equals sign does it have a certain value. It's value is determined by the value on the other side of the equals sign.

Constant - Any number that is not a variable.

Expression - A 'mathematical sentence' that does NOT have an equals sign. (x+5 instead of x+5=10.) Think of this like a recipe to make ANY cake using the ingredients given to you.

Equation - A 'mathematical sentence' that DOES have an equals sign. (x+5=1.) Think of this like a recipe to make a SPECIFIC cake.

Notation - In mathematics, this describes the set of symbols and numbers and how they are arranged to make logical sense. (x+5 instead of 'a number added to five'. Notation also helps to make a lot of information much more readable.

Isolate the variable - You'll hear this a lot, but all it means is 'get the variable on one side and the constants on the other side.' x+5=10 is not solved. x=5 is solved.

## Lesson

Zoey and Pual put three eggs on each side of a scale. When Zoey took an egg away on one side the scale, it tipped. When Pual took an egg from the other side of the scale, it is balanced again. The same thing can be used in math too.

What is ${\displaystyle y}$ in this equation?

${\displaystyle 2+y=7}$

We want to know what ${\displaystyle y}$ is, so we want to make ${\displaystyle y}$ by itself on one side of the equal sign.

First subtract 2 from both sides.

${\displaystyle 2-2+y=7-2}$

After we subtracted, ${\displaystyle y}$ is by itself and we can see that ${\displaystyle y}$ equals

${\displaystyle y=5}$

## Example Problems

Example 1

${\displaystyle 3+x-4=4}$

Add 4 to each side to get rid of the -4.

${\displaystyle 3+x-4+4=4+4}$

${\displaystyle 3+x=8}$

Subtract 3 from each side of the equation.

${\displaystyle 3+x-3=8-3}$

${\displaystyle x=5}$

## Practice Games

put links here to games that reinforce these skills

## Practice Problems

1 ${\displaystyle x+1=4}$

2 ${\displaystyle x-1=4}$