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 = c, where a, b, and c are constants.

Front

How do you isolate a variable in a linear 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 does it mean to solve for x in an equation?

Back

Solving for x means finding the value of x that makes the equation true.

Front

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

Back

The solution is x = 22/3.

Front

How do you solve the equation 2x = x + 3?

Back

Subtract x from both sides to get x = 3.

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

What is the equivalent expression for 'eight less than three times a number'?

Back

The expression is 3x - 8.

Front

How do you set up the equation for 'ten more than one and a half times the same number'?

Back

The expression is 1.5x + 10.

Front

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

Back

The solution is x = 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.