A.5A - Solve One Variable 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 that makes the equation true.

Front

What is the principle of equality in solving equations?

Back

The principle of equality states that if you perform the same operation on both sides of an equation, the two sides remain equal.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you need to perform inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving the equation -5 - (-7 - 4x) = -2(3x - 4)?

Back

The first step is to simplify both sides of the equation by distributing and combining like terms.

Front

What is the solution to the equation 2(40 - 5y) = 10y + 5(1 - y)?

Back

The solution is y = 5.

Front

How do you check if your solution to a linear equation is correct?

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 0.3(12x - 16) = 0.4(12 - 3x)?

Back

The solution is x = 2.

Front

What does it mean for an equation to have no solution?

Back

An equation has no solution when the variable cancels out and results in a false statement, such as 0 = 5.

Front

What is the solution to the equation 0.75(x + 20) = 2 + 0.5(x - 2)?

Back

The solution is x = -56.