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
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
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
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