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 (usually x) that makes the equation true.

Front

What is the first step in solving the equation 2x + 3 = 7?

Back

The first step is to isolate the term with the variable by subtracting 3 from both sides, resulting in 2x = 4.

Front

How do you isolate the variable in the equation 2x = 4?

Back

To isolate x, divide both sides of the equation by 2, giving x = 2.

Front

What is the solution to the equation x - 5 = 10?

Back

The solution is x = 15, found by adding 5 to both sides of the equation.

Front

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

Back

An equation has no solution when there is no value for the variable that can make the equation true, such as 2x + 3 = 2x + 5.

Front

What is the solution to the equation 3(x + 2) = 15?

Back

The solution is x = 3, found by first dividing both sides by 3, then subtracting 2.

Front

What is a variable in a linear equation?

Back

A variable is a symbol (usually x) that represents an unknown value in an equation.

Front

What does it mean to check your solution?

Back

To check your solution means to substitute the value back into the original equation to verify that both sides are equal.

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.