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 that makes the equation true.

Front

What is the first step in solving the equation 2(2x + 3) = -6(x + 9)?

Back

Distribute the numbers outside the parentheses: 4x + 6 = -6x - 54.

Front

How do you isolate the variable in the equation 6(2x + 1) = 18?

Back

First, simplify to get 12x + 6 = 18, then subtract 6 from both sides to get 12x = 12, and finally divide by 12 to find x = 1.

Front

What is the solution to the equation 10 = 3x - 12?

Back

The solution is x = 22/3.

Front

What is the process to combine like terms in the equation 8x + 2 + 3x + 5 = x + 12?

Back

Combine 8x and 3x to get 11x, and combine 2 and 5 to get 7, resulting in 11x + 7 = x + 12.

Front

What is the final step to solve for x in the equation 3(x - 2) = 18?

Back

First, distribute to get 3x - 6 = 18, then add 6 to both sides to get 3x = 24, and finally divide by 3 to find x = 8.

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 across a sum or difference, which simplifies the equation.

Front

What is a coefficient in a linear equation?

Back

A coefficient is a numerical factor that multiplies a variable, such as the '2' in 2x.