x on Both Sides
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 22 of 64.
An inequality can have x on both sides. To solve 3x + 2 > x + 8, first collect the x-terms on one side. Subtract x from both sides. An x-term is subtracted like any number, and subtracting never flips the sign. Then move the numbers to the other side, and divide.
2x + 2 > 8
2x > 6
x > 3
Check with a number above 3, such as 4. The left side is 3 × 4 + 2 = 14 and the right side is 4 + 8 = 12. Since 14 is greater than 12, the answer works.
The steps are the same as for an equation with x on both sides. Move the x-terms to one side, move the numbers to the other side, then divide. Each of these steps is an addition, a subtraction or a division by a positive number, so the sign keeps its direction.
Challenge
EasySolve the inequality 4x + 3 >= x + 12 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