Solving an equation using addition and solving an inequality using addition are very similar processes. Let's recall the Addition Property of Equality.

Addition Property of Equality
Adding the same number to each side of an equation produces an equivalent equation.

Now, we can compare it with the Addition Property of Inequality.

Addition Property of Inequality
Adding the same number to each side of an inequality produces an equivalent inequality.

As we can see, in both cases, after performing addition on both sides we obtain equivalent expressions. This means that we can apply the inverse operation of addition in both equations and inequalities in the same way. Let's look at some examples!

Solving an Equation Using Addition

As an example, we will solve

x - 2 = 8 .

To do so, we will isolate

x

by adding

2

to both sides of the equation.

x - 2 = 8

AddEqn

$LHS + 2 = RHS + 2$

x - 2 + 2 = 8 + 2

AddTerms

Add terms

x = 10

Solving an Inequality Using Addition

This time, we will consider

x - 2 > 8 .

To solve this inequality, we will isolate

x

by once again adding

2

to both sides of the inequality.

x - 2 > 8

AddIneq

$LHS + 2 > RHS + 2$

x - 2 + 2 > 8 + 2

AddTerms

Add terms

x > 10

Conclusion

As shown in our examples, we can see that solving equations and inequalities with addition is very similar. In both cases, we obtained equivalent statements after using the same operations.

Exercise

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