Solving Multi-Step Equations (with Distributive Property)

Front

What is a multi-step equation?

Back

An equation that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, and division.

Front

What is the Distributive Property?

Back

A property that states a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

Solve: 3x + 15 = 3(x + 5)

Back

All real numbers (infinite solutions).

Front

What is a let statement in word problems?

Back

A statement that defines a variable to represent an unknown quantity, helping to set up the equation.

Front

Let x = total # of rooms cleaned. What is the equation for Pristine House Cleaners?

Back

Total cost = 19.85 + 32x.

Front

Let x = total # of rooms cleaned. What is the equation for Sparkle House Cleaners?

Back

Total cost = 61.85 + 18x.

Front

How do you find the number of rooms where both cleaners cost the same?

Back

Set the equations equal to each other and solve for x.

Front

If Mrs. Burrell spends $35 on donuts and chocolate milk, how do you set up the equation?

Back

3d + 2 = 35, where d is the number of donuts.

Front

Solve: 4(a + 3) = -32

Back

a = -11.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation.