Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c 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 (usually x) that makes the equation true.

Front

What is the first step in solving the equation 3(5x + 10) + 10 = 6x - (x + 10)?

Back

Distribute the 3 on the left side: 15x + 30 + 10 = 6x - x - 10.

Front

What is the solution to the equation 2x + 5 = 12?

Back

x = 3.5.

Front

How do you isolate the variable in the equation 2(3x + 4) + 2 = 4 + 3x?

Back

First, simplify both sides, then move all terms involving x to one side and constant terms to the other.

Front

What is the solution to the equation 8x + 2 + 3x + 5 = x + 12?

Back

x = 1/2.

Front

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

Back

Combining like terms involves adding or subtracting coefficients of the same variable to simplify the equation.

Front

What is the solution to the equation 12 = 20x - 18?

Back

x = 2.

Front

What does it mean to check your solution in a linear equation?

Back

Checking your solution means substituting the value back into the original equation to verify that both sides are equal.

Front

What is the importance of the distributive property in solving equations?

Back

The distributive property allows you to eliminate parentheses by multiplying a term outside the parentheses by each term inside.