Solving Equations with Special Cases

Front

What is a special case in solving equations?

Back

A special case occurs when an equation has either infinitely many solutions or no solution at all, rather than a single unique solution.

Front

What does it mean if an equation has many solutions?

Back

It means that any value of the variable satisfies the equation, often resulting from equivalent expressions on both sides.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value of the variable that can satisfy the equation, often resulting from contradictory statements.

Front

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

Back

Many Solutions

Front

Solve the equation: 4(r + 2) - 3 = 4r - 11

Back

No Solution

Front

Complete the equation so it has one solution of x = 3: 2(5x - 7) = 2x + _____

Back

The missing value is 10.

Front

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

Back

x = 12, one solution.

Front

For the equation 3(10x + 5) = 30x + n, which value of n will create an equation with infinitely many solutions?

Back

n = 15.

Front

What is the first step in solving an equation?

Back

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

Front

What is the purpose of isolating the variable in an equation?

Back

Isolating the variable helps to find its value by getting it alone on one side of the equation.