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 an 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 to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

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

Back

x = 12

Front

What is the solution to the equation 9x + 2 = 5?

Back

x = 1/3

Front

What is the solution to the equation 10 = 3x - 12?

Back

x = 22/3

Front

What is the first step in solving the equation 3x + 4 = 10?

Back

Subtract 4 from both sides to isolate the term with the variable.

Front

What is the purpose of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation.

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.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation, often resulting in a contradiction.