Solve 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 2(3x + 4) + 2 = 4 + 3x?

Back

Distribute the 2 on the left side: 6x + 8 + 2 = 4 + 3x.

Front

How do you isolate the variable x in the equation x - 23 = 17?

Back

Add 23 to both sides: x = 17 + 23, which simplifies to x = 40.

Front

What is the solution to the equation 4x + 1 = 7x - 5?

Back

The solution is x = 2.

Front

How do you solve the equation 2x + 5 = 12?

Back

Subtract 5 from both sides: 2x = 12 - 5, then divide by 2: x = 3.5.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value of the variable that satisfies the equation.

Front

What is the solution to the equation 1/2x + 2 = 3x + 2?

Back

The equation has one solution, which can be found by simplifying and solving for x.

Front

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

Back

To verify that the value found for the variable makes the original equation true.

Front

What is the general form of a linear equation?

Back

The general form is ax + b = c, where a, b, and c are real numbers and a ≠ 0.