# Solving equations using subtraction

When solving equations using subtraction, these equations will have the form x + b = c. Recall that ax + b = c is a linear equation.

Therefore, the equation x + b = c is also a linear equation with a = 1.

In order to this see this, notice that 1x = x. Thus, we can rewrite x + b = c as 1x + b = c and it will have the same format as ax + b = c.

You can solve x + b = c in one step.

When solving one step equation of the form x + b = c, subtract b from both sides of the equation.

x + b = c

x + b - b = c - b

x + 0 = c - b

x = c - b

## A few of examples showing how to solve equations using subtraction.

We will illustrate with 3 examples.

Example #1: Solve the equation x + 3 = 8 for x using subtraction. Alternatively, you do not need to put the -3 beneath the 3. You can also put the -3 next to it.

x + 3 = 8

x + 3 - 3 = 8 - 3

x + 0 = 5

x = 5

Example #2: Solve the equation x + 5 = 10 for x using subtraction. Alternatively, you do not need to put the -5 beneath the 5. You can also put the -5 next to it.

x + 5 = 10

x + 5 - 5 = 10 - 5

x + 0 = 5

x = 5

Example #3: Solve the equation x + 5 = -10 for x using subtraction. Alternatively, you do not need to put the -5 beneath the 5. You can also put the -5 next to it.

x + 5 = -10

x + 5 - 5 = -10 - 5

x + 0 = -15

x = -15

## A quick way to solve equations of the form x + b = c

As already demonstrated above, if x + b = c, then x = c - b. Here are some examples.

If x + 6 = 2, then x = 2 - 6 = -4

If x + -4 = 4, then x = 4 - -4 = 4 + 4 = 8

If x + 2 = 9, then x = 9 - 2 = 7

If x + -2 = -9, then x = -9 - -2 = -9 + 2 = -7

## Solving equations using subtraction. Can you get 100% on this quiz?

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