Reading It Backwards
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 4 of 64.
Sometimes the unknown ends up on the right: 7 < x + 3. Subtracting 3 from both sides gives 4 < x, which is perfectly true, just written backwards. "4 is less than x" means "x is greater than 4", so it is usually written with x first:
x > 4
Swapping the two sides reverses the sign: 4 < x becomes x > 4, and 9 >= x becomes x <= 9. Nothing about the numbers changed; the sentence was read from the other end.
Reading a sentence from the other end changes nothing about its meaning. 4 < x and x > 4 describe the same numbers: every number above 4. Writing x first is only the tidier habit, and the one the rest of this course keeps.
Challenge
Solve 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