Reading It Backwards
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 4 of 64.
Sometimes the unknown is on the right side, as in 7 < x + 3. Subtract 3 from both sides to get 4 < x. This answer is correct, but it is written with the number first. "4 is less than x" means "x is greater than 4", so the answer is usually written with x first:
x > 4
When you swap the two sides, you must reverse the sign. 4 < x becomes x > 4, and 9 >= x becomes x <= 9. The numbers do not change. You only read the inequality from the other end.
The inequalities 4 < x and x > 4 describe the same numbers, all the numbers greater than 4. Swapping the sides reverses the sign, but it does not change the meaning of the inequality.
Challenge
EasySolve the inequality 10 > x + 6 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