Chains with Fractions

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 35 of 64.

0 <= x/2 < 3: half of x is between 0 and 3, so x is between 0 and 6. Multiplying all parts by 2 says it:

0 <= x < 6

A positive multiplier keeps both signs. Had the middle been -x/2, multiplying by -2 would flip both.

The same care as ever: a fraction is undone by multiplying by its denominator, and the sign question is "positive or negative multiplier?", not "how big?".

Challenge

Solve the compound inequality -2 < x/3 <= 1 for x.

Try it yourself

-2 < x/3 <= 1

Solve for x

Test yourself

This 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 Signs A Picture on a Line Closed or Open Reading It Backwards Recap: What an Inequality Is

4Two-Step Inequalities

Two Steps Subtract, Then Flip With a Fraction A Bracket on the Way Recap: Two-Step Inequalities

7Between Two Numbers

Two Conditions at Once Solving a Chain Two Moves on All Parts When the Chain FlipsChains with FractionsRecap: Between Two Numbers

10Absolute Value Inequalities

Less Than: Between Between, Shifted Greater Than: Outside Outside, Shifted Isolate, Then Split Always or Never Recap: Absolute Inequalities

2Adding and Subtracting

Add to Both Sides Subtract from Both Sides Negatives in the Mix Solve, Then Draw Recap: Adding and Subtracting

5Variables on Both Sides

x on Both Sides Gather Toward the Larger Brackets First Always True, Never True Recap: Variables on Both Sides

8One or the Other

Either Works Solving Each Part And versus Or Recap: One or the Other

11From Words to Inequalities

At Least, At Most More Than A Budget That Shrinks Two Limits Recap: From Words