Add to Both Sides
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 6 of 64.
If 3 < 7, then adding 2 to both numbers gives 5 < 9: still true, still the same way round. Adding the same amount to both sides of an inequality never disturbs it. That is the first rule, and it is what lets you undo a subtraction.
x - 4 > 3: add 4 to both sides.
x - 4 + 4 > 3 + 4
x > 7
The sign did not move and did not change; only the numbers around x did. Check with a number: 10 is above 7, and 10 - 4 = 6 is indeed greater than 3. Try 5, which is below 7: 5 - 4 = 1 is not greater than 3. The range x > 7 is exactly right.
Challenge
Solve the inequality x - 6 > 1 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