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 solution to the equation 5n + 34 = −2(1− 7n)?

Back

n = 4

Front

How many solutions does the equation −5x + 5 − 4x = −1 − 9x have?

Back

No Solutions

Front

What is the solution to the equation 5 + 4x − 7 = 4x − 2 − x?

Back

x = 0

Front

What is the solution to the equation 3m = 5(m + 3) − 3?

Back

m = -6

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value of the variable satisfies the equation, meaning the two sides of the equation are always equal.

Front

What is the significance of the equation -10y - 6 = -10y - 6?

Back

This equation has infinite solutions because both sides are identical, meaning any value of y will satisfy the equation.

Front

What is the first step in solving the equation 5n + 34 = −2(1− 7n)?

Back

Distribute the -2 on the right side to simplify the equation.

Front

What is a contradiction in linear equations?

Back

A contradiction occurs when an equation simplifies to a false statement, indicating that there are no solutions.