Negatives in the Mix
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 8 of 64.
Negative numbers on either side do not change the method. To solve x - 7 < -2, add 7 to both sides:
x < -2 + 7
x < 5
To add 7 to -2, start at -2 on the number line and go up 7 to reach 5. The picture of the answer is an open dot at 5 with shading to the left.
After solving, you can check a number from your answer in the original inequality. For x < 5, try 0. Then 0 - 7 = -7, and -7 is less than -2, so 0 works. This check can show a mistake. It does not prove that the whole range is right, so also check the endpoint and the direction of the sign.
Challenge
EasySolve the inequality x - 3 < -8 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