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 7x + 5 + x - 3 + x = 5?

Back

Combine like terms: 7x + x + x = 9x, so the equation becomes 9x + 2 = 5.

Front

How do you isolate the variable in the equation 7x + 5 + x - 3 + x = 5?

Back

Subtract 2 from both sides to get 9x = 3, then divide by 9 to find x = 1/3.

Front

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

Back

Subtract 3x from both sides to get 4x = 24, then divide by 4 to find x = 6.

Front

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

Back

Subtract 4x from both sides to get 1 = 3x - 5, then add 5 to both sides to find 6 = 3x, so x = 2.

Front

What is the solution to the equation 5 + 3x = 8x - 15?

Back

Subtract 3x from both sides to get 5 = 5x - 15, then add 15 to both sides to find 20 = 5x, so x = 4.

Front

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

Back

Add 18 to both sides to get 30 = 20x, then divide by 20 to find x = 1.5 or x = 2.

Front

What does 'combining like terms' mean?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

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 it is correct.