A Bracket on the Way
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 20 of 64.
In 2(x - 3) >= 4, the bracket is multiplied by 2. When the other side divides by 2 with no remainder, the quickest first step is to divide both sides by 2. The bracket is no longer needed. Then add 3 to both sides:
x - 3 >= 2
x >= 5
You can also distribute first to get 2x - 6 >= 4. Then add 6 to both sides and divide by 2. The answer is the same.
Brackets, fractions, added numbers and coefficients are each undone by the opposite operation, in the same order as for an equation. The one new rule in this section is the flip. The sign flips only when you multiply or divide by a negative number.
Challenge
EasySolve 3(x + 1) <= 12.
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