Solving Inequalities with Addition

Solving an inequality is very similar to solving an equation. The only difference is that sometimes you have to reverse the inequality symbol, which we'll discuss later.

Therefore, if you have a number added to the variable, you add the opposite to both sides, just like an equation.


x+8≤5 The 8 is being added so we must add -8 to both sides.


x≤-3 This is our answer. Any number that is less that or equal to -3 will make the original inequality true.

Note: If you want to switch sides of an equation, you must reverse the inequality symbol. Let's look at
an example to see why. We all know that 2<5, but if we want to switch the sides and put 5 on the left and 2 on the right, we cannot just switch them and keep the symbol the same because we would get 5<2, which is false. If we want to switch sides, we must also switch the symbol: 5>2 in order for the statement to stay correct. This is also true when variables are involved.


-4>x-9If we want to switch this so the variable is on the left, we must also reverse the symbol.

x-9<-4We can now proceed as normal.



Practice:Solve the following inequalities.

1) x+7>2

2) y-8≤12

3) x+3≥-1

4) -2<4+a

5) -2+n≤6

Answers: 1)) x>-52) y≤203) x≥-4 4) -6<a or a>-65) n≤8

Related Links:
Algebra Topics
Introduction to Inequalities
Graphing linear inequalities
Solving inequalities with addition
Solving inequalities with multiplication/division
Solving multi-step inequalities
Solving Inequalities