x on Both Sides
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 22 of 64.
3x + 2 > x + 8: gather the x-terms on one side by subtracting x from both sides (an x-term is subtracted like any number, and subtracting never flips), then the numbers, then divide.
2x + 2 > 8
2x > 6
x > 3
Check: 4 is above 3; 3 × 4 + 2 = 14 and 4 + 8 = 12, and 14 is greater than 12.
It is the equation routine with an inequality sign: x-terms to one side, numbers to the other, divide. Because every move here is an addition, a subtraction or a division by a positive, the sign never changes direction.
Challenge
Solve 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