Solving Each Part
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 38 of 64.
When each part of an "or" inequality needs solving, solve the two parts separately and keep the word "or" between the answers. Take 2x + 1 < -3 or 3x - 2 > 7. For the first part, subtract 1 from both sides, then divide by 2:
2x < -4
x < -2
For the second part, add 2 to both sides, then divide by 3:
3x > 9
x > 3
The solution is x < -2 or x > 3. These are the two rays from the previous lesson.
Each part is an ordinary inequality, and the ordinary rules apply to it. If you divide a part by a negative number, its sign flips. The word "or" tells you to keep both answers. It does not tell you to combine them into one inequality.
Challenge
MediumSolve x + 1 < 0 or 2x > 8, and show the solutions on the number line.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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