Solving Two-Step Equations and Equations with Parentheses

Front

What is a two-step equation?

Back

A two-step equation is an algebraic equation that requires two operations to solve for the variable. It typically involves isolating the variable by performing an inverse operation twice.

Front

How do you isolate a variable in a two-step equation?

Back

To isolate a variable in a two-step equation, perform the inverse operations in the reverse order of operations: first, eliminate any constant term by adding or subtracting, and then eliminate the coefficient by multiplying or dividing.

Front

What is the first step to solve the equation 4c - 6 = 2?

Back

The first step is to add 6 to both sides of the equation to eliminate the constant term: 4c - 6 + 6 = 2 + 6, which simplifies to 4c = 8.

Front

What is the solution to the equation 4c - 6 = 2?

Back

The solution is c = 2.

Front

What does it mean to solve an equation with parentheses?

Back

Solving an equation with parentheses involves using the distributive property to eliminate the parentheses before isolating the variable.

Front

How do you solve the equation 9 = 2(5x - 3)?

Back

First, apply the distributive property: 9 = 10x - 6. Then, add 6 to both sides: 15 = 10x, and finally divide by 10 to find x = 1.5 or x = 3/2.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a set of parentheses.

Front

How do you combine like terms in the equation -2x - 7 + 3x = 10?

Back

Combine the x terms: (-2x + 3x) = x, so the equation simplifies to x - 7 = 10.

Front

What is the solution to the equation -2x - 7 + 3x = 10?

Back

The solution is x = 17.

Front

How do you solve the equation -(n - 8) = -2?

Back

First, distribute the negative sign: -n + 8 = -2. Then, subtract 8 from both sides: -n = -10, and finally multiply by -1 to find n = 10.