Two Conditions at Once
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 31 of 64.
"x is greater than 1 and x is less than 5" is two conditions that must both hold. Written as one line, with x in the middle:
1 < x < 5
Read it from the middle: x is above 1 and below 5. The solutions are the numbers strictly between 1 and 5, a segment of the number line with an open dot at each end.
1 < x < 5: between 1 and 5, both ends open
The ends can be closed too. -2 <= x < 3 includes -2 (filled dot) but not 3 (open dot). A chain always reads one way, from small to large: 1 < x < 5 or 5 > x > 1, never a mixture of < and > in one chain.
Challenge
Show the solutions of -2 <= x < 3 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 Inequalities7Between Two Numbers
Two Conditions at OnceSolving a ChainTwo Moves on All PartsWhen the Chain FlipsChains with FractionsRecap: Between Two Numbers2Adding 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