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

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

What is the solution to the equation 2 - 4x = 3x - 12?

Back

The solution is x = 2.

Front

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

Back

First, divide both sides by 6 to get 2x + 1 = 3, then subtract 1 from both sides to isolate 2x.

Front

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

Back

The solution is x = 2.

Front

What is the process of combining like terms in an equation?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

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

Back

The solution is x = 4.

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 equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides of the equation are equivalent.