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 4x + 1 = 7x - 5?

Back

The first step is to isolate the variable x by moving all terms involving x to one side of the equation and constant terms to the other side.

Front

Solve for x: 4x + 1 = 7x - 5

Back

x = 2

Front

What is the solution to the equation 7x - 3x - 8 = 24?

Back

x = 8

Front

How do you simplify the equation 10 = 3x - 12 to find x?

Back

Add 12 to both sides to get 22 = 3x, then divide by 3 to find x = 22/3.

Front

What is the solution to the equation 3(x - 2) = 18?

Back

x = 8

Front

How do you 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 solution for x in the equation 8x + 2 + 3x + 5 = x + 12?

Back

x = 1/2

Front

What is the importance of checking your solution in a linear equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming its correctness.