Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = 0, where a and b are constants.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable that makes the equation true.

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 perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation 6(2x + 1) = 18?

Back

The first step is to apply the distributive property: 12x + 6 = 18.

Front

What is the solution to the equation 2(3x + 4) + 2 = 4 + 3x?

Back

The solution is x = -2.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.

Front

What is the purpose of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to solve.

Front

How do you check if your solution to a linear equation is correct?

Back

You substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 7 - 2(10x + 1) = 25?

Back

The solution is x = -1.