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 that makes the equation true.

Front

What is the first step in solving the equation 3(x - 2) = 18?

Back

Distribute the 3 to both terms inside the parentheses: 3x - 6 = 18.

Front

How do you isolate the variable in the equation 5 + 3x = 8x - 15?

Back

Subtract 3x from both sides to get 5 = 5x - 15, then add 15 to both sides to isolate the term with x.

Front

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

Back

The solution is x = 2.

Front

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

Back

Combining like terms simplifies the equation, making it easier to solve.

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 significance of the equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides have the same value.

Front

What is the first step in solving for w in the equation 3w + 5 = 14?

Back

Subtract 5 from both sides of the equation.

Front

What is the solution to the equation 2(2x + 3) = -6(x + 9)?

Back

The solution is x = -6.