2 Step Inequalities - Word Problems - Adv.

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality x/4 + 2 > -3?

Back

First, subtract 2 from both sides: x/4 > -5. Then, multiply both sides by 4: x > -20.

Front

What does the inequality 3x + 20 ≤ 120 represent in a word problem?

Back

It represents a situation where the total cost of an item (3 times the price of the skirt plus $20) must be less than or equal to $120.

Front

How do you interpret the inequality 5x + 10 ≥ 100?

Back

This inequality means that the total amount earned from babysitting (5 dollars per hour times the number of hours plus $10) must be at least $100.

Front

What is the first step in solving the inequality 71 - 3.5x = 40?

Back

The first step is to isolate the variable term by subtracting 71 from both sides: -3.5x = 40 - 71.

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What does the solution x < -20 indicate in a word problem?

Back

It indicates that the value of x must be less than -20 to satisfy the inequality.

Front

What is the significance of the inequality symbol in 6 > x?

Back

The symbol '>' indicates that 6 is greater than x, meaning x can take any value less than 6.

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How do you represent a situation where a temperature must not exceed a certain value using an inequality?

Back

You can use an inequality like x ≤ maximum temperature, where x represents the current temperature.

Front

What is the process for graphing a two-step inequality?

Back

1. Solve the inequality for the variable. 2. Plot the boundary line (dashed for < or >, solid for ≤ or ≥). 3. Shade the appropriate region.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality, often resulting from contradictory statements.