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Expressions, Equations, and Inequalities

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Expressions, Equations, and Inequalities

Read each item carefully. A variable expression has no equals or comparison sign; an equation states that two quantities are equal; an inequality uses signs such as <, >, ≤, or ≥.

Classify the statements

Choose the correct type for each mathematical statement.

1.How many terms are in 6y − 4?

One
Two
Three

2.What kind of mathematical statement is 5a + 9 = 34?

Variable expression
Equation
Comparison statement

3.What kind of mathematical statement is 3p − 2 < 16?

Variable expression
Equation
Comparison statement

4.Select every statement that uses an equals sign to show two quantities are equal.

8n + 1 = 25
4n − 7
2n ≥ 10
9 + n = 18

Write algebra from situations

Use the variable named in each question. Include the operation or comparison shown by the situation.

5.A club buys notebooks for $4 each and has $32 to spend. Write an algebraic form for the cost of n notebooks.

6.Using the notebook situation, write a number statement that represents spending exactly $32 on n notebooks.

7.Using the notebook situation, write an inequality that represents spending no more than $32 on n notebooks.

8.A bike rental costs a $6 sign-up fee plus $3 for each hour. Write an algebraic form for the cost of h hours of rental.

9.For the bike rental, Isabella has $24 to spend. Write an inequality showing which rental times h Isabella can afford.

10.A greenhouse needs a temperature of at least 70°F. Write an inequality using t for the temperature.

Explain and apply

Show that you understand how different algebraic statements are used.

11.In your own words, explain one difference between a variable expression and a statement of equality. Include an example of each.

12.A student has $18 and wants to buy pencils that cost $2 each. Let p be the number of pencils. Write an algebraic form for the cost, an inequality for staying within the budget, and an equation for spending exactly $18.

13.Avery's first three quiz scores are 82, 91, and 89. Avery wants an average score of at least 90 after four quizzes. If x is the fourth score, write an inequality to represent this goal.