Solving equations using addition

When solving equations using addition, 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 and a negative sign in front of the b.

To see this, notice that 1x = x and - = + -

Thus, we can rewrite x - b = c as 1x + -b = c so that it has the format ax + b = c.

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

When solving one step equation of the form x - b = c, rewrite x - b = c as x + -b = c and then add b to both sides of the equation.

x + -b = c

x + -b + b = c + b

x + 0 = c + b

x = c + b

A couple of examples showing how to solve equations using addition.

We will illustrate with two examples.

Example #1: Solve the equation x - 2 = 8 using addition.

Example #2: Solve the equation x - 4 = -6 using addition.

You could also solve the equation x - 2 = 8 as shown below as well.

x - 2 = 8
x + -2 = 8
x + -2 + 2 = 8 + 2
x + 0 = 10
x = 10

You could also solve the equation x - 4 = -6 as shown below as well.

x - 4 = -6
x + -4 = -6
x + -4 + 4 = -6 + 4
x + 0 = -2
x = -2

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 - 1 = -5, then x = -5 + 1 = -4

If x - 22 = -2, then x = -2 + 22 = 20

If x - 5 = 4, then x = 4 + 5 = 9