Distance from Zero
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 41 of 64.
The absolute value of a number is its distance from zero on the number line. A distance has no sign, so |3| = 3 and |-3| = 3. Both 3 and -3 are three steps from zero. A distance is never negative, so an absolute value is never negative.
3 and -3 are both three steps from 0: |3| = |-3| = 3
When there is an expression inside the absolute value bars, work it out first: |2 - 7| = |-5| = 5. The bars keep the size of the number and drop its sign. Every positive number is the absolute value of two numbers, one positive and one negative. Only zero has an absolute value of zero.
Challenge
MediumCompute |-9| + |4|.
Try it yourself
Simplify the expression
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 Solutions9Absolute Value Equations
Distance from ZeroThe Equation |x| = 3Distance from a PointIsolate the Bars FirstA Coefficient InsideNo Solution, One SolutionRecap: Absolute Equations