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

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 -5(2x - 9) = 2(x - 8) - 11?

Back

x = 6

Front

What is the solution to the equation -8 - x = x - 4x?

Back

x = 4

Front

What does it mean if a linear equation has infinitely many solutions?

Back

It means that there are an infinite number of values for the variable that satisfy the equation, often because the equation simplifies to a true statement.

Front

What is the solution to the equation 8x + 4 = 4(2x + 1)?

Back

Infinitely Many Solutions

Front

What does it mean if a linear equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation, often because it simplifies to a contradiction.

Front

What is the solution to the equation 6 + 3x = x - 8?

Back

One Unique Solution

Front

What is the solution to the equation 6x + 7 = 13 + 7x?

Back

x = -6

Front

What is the first step in solving the equation 6 + 3x = x - 8?

Back

Isolate the variable by moving all terms involving x to one side and constant terms to the other side.