Brackets First
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 24 of 64.
When an inequality has a bracket, distribute first to remove the bracket. To solve 2(x - 1) <= x + 3, multiply out the 2, then collect the x-terms and the numbers.
2x - 2 <= x + 3
x - 2 <= 3
x <= 5
Check with a number below 5, such as 0. The left side is 2(0 - 1) = -2 and the right side is 0 + 3 = 3. Since -2 is less than or equal to 3, the answer works.
The order of steps is the same as for an equation with brackets. Distribute, simplify each side, collect the x-terms on one side and the numbers on the other, then divide. The sign only flips if the last step divides by a negative coefficient.
Challenge
MediumSolve 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