Subtract from Both Sides
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 7 of 64.
Subtracting the same amount from both sides also keeps the inequality true and keeps its direction. To solve x + 5 <= 2, subtract 5 from both sides:
x + 5 - 5 <= 2 - 5
x <= -3
The answer is negative, and a negative answer is fine. Every number up to and including -3 works. Check the endpoint: -3 + 5 = 2, and 2 is less than or equal to 2.
Adding and subtracting are the two steps that never change the sign. Whatever you add to one side, add to the other side too. Whatever you subtract from one side, subtract from the other side too. The sign stays as it was.
Challenge
EasySolve the inequality x + 9 <= 4 for x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Inequalities & Absolute Value
1What an Inequality Is
The Four SignsA Picture on a LineClosed or OpenReading It BackwardsRecap: What an Inequality Is4Two-Step Inequalities
Two StepsSubtract, Then FlipWith a FractionA Bracket on the WayRecap: Two-Step Inequalities2Adding and Subtracting
Add to Both SidesSubtract from Both SidesNegatives in the MixSolve, Then DrawRecap: Adding and Subtracting5Variables on Both Sides
x on Both SidesGather Toward the LargerBrackets FirstAlways True, Never TrueRecap: Variables on Both Sides11From Words to Inequalities
At Least, At MostMore ThanA Budget That ShrinksTwo LimitsRecap: From Words3Multiplying and Dividing
Divide by a PositiveMultiply by a PositiveThe FlipDividing by a NegativeNegative FractionsRecap: Multiply and Divide6Graphing Solutions
From Inequality to PictureIs the Endpoint In?A Flip on the LineRecap: Graphing Solutions