HSA.CED.A.1: Create equations and inequalities — Practice

Work through problems with immediate feedback

Warm-Up: Review What You Know

These problems review skills from earlier courses.

A recipe uses a certain number of cups of flour. After using 2 cups, 5 cups remain. Which statement best defines the variable for this problem?

Let $x$ = the total cups of flour in the recipe, in cups.

Let $x$ = flour, since flour is the ingredient the problem is about.

Let $x$ = 7, since 2 cups used plus 5 cups remaining totals 7 cups.

Let $x$ = the amount used, since that's the quantity mentioned first in the problem.

Which algebraic statement is an equation (not just an expression)?

$3x + 7$

$3x \cdot 7$

$3(x + 7)$

$3x + 7 = 22$

Which number line correctly shows the solution set for $x \leq 4$ ?

A closed dot at 4, with an arrow pointing to the right.

An open dot at 4, with an arrow pointing to the left.

A closed dot at 4, with an arrow pointing to the left.

An open dot at 4, with an arrow pointing to the right.

Fluency Practice

A cell phone plan charges $30 per month plus $0.10 per text message. Keiko's bill was $47.50 last month. Let $t$ = the number of text messages sent. Which equation correctly models this situation?

$30 + 0.10 = 47.50$

$30 + 0.10t$

$0.10t = 47.50$

$30 + 0.10t = 47.50$

A store needs to earn at least $800 from hat sales. Hats sell for $25 each. Let $h$ = the number of hats sold. Which inequality correctly models this situation?

$25h \geq 800$

$25h \leq 800$

$25h < 800$

$25h > 800$

A car rental charges $45 per day plus $0.20 per mile. Jordan rented a car for 1 day and the total cost was $73. Let $m$ = miles driven. Solve $45 + 0.20m = 73$ for $m$ . How many miles did Jordan drive?

A ball is dropped from a height of 100 feet. Its height after $t$ seconds is $h = -16t^2 + 100$ . Set $h = 0$ and solve for $t$ to find when the ball hits the ground. Give your answer rounded to the nearest tenth of a second. (Take only the positive solution.)

An investment of $500 grows at 4% annual interest, compounded annually. Let $t$ = years. Which equation models when the investment reaches $608.33?

$500 + 0.04t = 608.33$

$500 \cdot (0.04)^t = 608.33$

$500 \cdot (1.04)^t = 608.33$

$500t = 608.33$

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Exercises: Create Equations and Inequalities in One Variable

Warm-Up: Review What You Know

Fluency Practice