Multi-step Equations

Front

What is a multi-step equation?

Back

An equation that requires more than one step to solve, often involving combining like terms, using the distributive property, and isolating the variable.

Front

How do you solve the equation -166=7x+3(6x+3)?

Back

First, distribute: -166 = 7x + 18x + 9. Combine like terms: -166 = 25x + 9. Then, isolate x: 25x = -175, so x = -7.

Front

What is the first step in solving the equation 14p - 8 = 22 + 20p?

Back

Add 8 to both sides to eliminate the constant on the left side: 14p = 30 + 20p.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation, often resulting in a contradiction.

Front

Solve for f: f - 4 = 6f + 26.

Back

Rearranging gives: f - 6f = 26 + 4, so -5f = 30, thus f = -6.

Front

What is the goal of solving multi-step equations?

Back

To find the value of the variable that makes the equation true.

Front

What is the distributive property?

Back

A property that states a(b + c) = ab + ac, used to eliminate parentheses in equations.

Front

How do you combine like terms in an equation?

Back

By adding or subtracting coefficients of the same variable to simplify the equation.

Front

What is an example of an equation with no solution?

Back

3(2x + 1) = 6x + 1, which simplifies to 6x + 3 = 6x + 1, leading to a contradiction.

Front

What is the importance of isolating the variable in an equation?

Back

Isolating the variable allows you to solve for its value, which is the ultimate goal of solving equations.