Solving Equations with Special Cases

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 if an equation has one solution?

Back

An equation has one solution if there is exactly one value of the variable that makes the equation true.

Front

What does it mean if an equation has many solutions?

Back

An equation has many solutions if any value of the variable makes the equation true, indicating that the two sides of the equation are equivalent.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there is no value of the variable that can make the equation true, indicating a contradiction.

Front

Solve the equation: 10x - 9 = 2x + 63

Back

x = 9, one solution.

Front

Solve the equation: 11x - 5 = 8x + 31

Back

x = 12, one solution.

Front

For the equation 3(10x + 5) = 30x + n, what value of n creates infinitely many solutions?

Back

n = 15.

Front

Solve the equation: 9y + 2 = 3(3y + 2) - 4

Back

Many Solutions.

Front

Solve the equation: 3(2x - 8) = 2(3x - 12)

Back

Many Solutions.

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation, if necessary, by distributing and combining like terms.