Multistep Equations and Word Problems Practice

Front

What is a multistep equation?

Back

A multistep equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

Front

How do you solve the equation 10(h + 1) - 4 = 76?

Back

1. Distribute: 10h + 10 - 4 = 76 2. Combine like terms: 10h + 6 = 76 3. Subtract 6 from both sides: 10h = 70 4. Divide by 10: h = 7.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you need to perform inverse operations to get the variable alone on one side of the equation.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

Solve for x: -118 = -5(4 + 7x) + 7

Back

1. Distribute: -118 = -20 - 35x + 7 2. Combine like terms: -118 = -13 - 35x 3. Add 13 to both sides: -105 = -35x 4. Divide by -35: x = 3.

Front

What is a word problem in mathematics?

Back

A word problem is a mathematical problem that is presented in the form of a story or real-life scenario, requiring interpretation and translation into a mathematical equation.

Front

Write an equation for the following scenario: Sophia has $35 to spend at the carnival, which costs $20 to enter and $0.50 per ticket.

Back

0.50x + 20 = 35, where x is the number of tickets.

Front

How do you set up an equation from a word problem?

Back

Identify the variables, determine the relationships between them, and translate the words into mathematical expressions.

Front

Solve for x: The area of a rectangle is 40 square cm. If the length is 10 cm, what is the width?

Back

Area = length × width, so 40 = 10 × x. Thus, x = 4.