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 for an equation to have a solution?

Back

An equation has a solution if there is a value for the variable that makes the equation true.

Front

What is the solution to the equation 3(x - 1) + 2(x + 3) = 13?

Back

x = 2

Front

How do you check if a value is a solution to an equation?

Back

Substitute the value back into the original equation. If both sides are equal, the value is a solution.

Front

What is the process to solve the equation -5k + 10 = -2k - 14?

Back

Combine like terms and isolate k: -5k + 2k = -14 - 10, which simplifies to -3k = -24, giving k = 8.

Front

Which equation has x = 2 as a solution?

Back

11 + x = 13

Front

What is the value of b that makes the equation 2b + 4 = 8 true?

Back

b = 2

Front

Solve the equation 3(x - 2) + 2(x + 1) = 6.

Back

x = 2

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.