Brackets First
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 24 of 64.
2(x - 1) <= x + 3: open the bracket first, then gather.
2x - 2 <= x + 3
x - 2 <= 3
x <= 5
Check: 0 is below 5; 2(0 - 1) = -2 and 0 + 3 = 3, and -2 is at most 3.
Distribute, tidy each side, gather across the sign, divide. Exactly the order from the equations chapter, and the sign only turns if a negative coefficient has to be divided away at the end.
Challenge
Solve the inequality 3(x + 1) > 2x + 7 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