Number of Solutions

Front

What is the definition of 'One Solution' in the context of equations?

Back

An equation has 'One Solution' when there is exactly one value of the variable that satisfies the equation.

Front

What does 'No Solution' mean in an equation?

Back

'No Solution' means that there is no value of the variable that can satisfy the equation, often because the two sides are contradictory.

Front

What does 'Infinite Solutions' indicate in an equation?

Back

'Infinite Solutions' indicates that any value of the variable satisfies the equation, meaning the two sides are equivalent for all values.

Front

Solve for b: 2b ‒ 5 = 9

Back

b = 7 (One Solution)

Front

Solve for q: –2q ‒ 3 = –2q ‒ 8

Back

No Solution (the equation simplifies to a contradiction)

Front

Solve for p: 8p ‒ 1 = 1 + 8p

Back

No Solution (the equation simplifies to a contradiction)

Front

Solve for m: 8m ‒ 4 ‒ 2m = 3(2m ‒ 1)

Back

No Solution (the equation simplifies to a contradiction)

Front

Solve for r: 6 + 9r = 9r + 6

Back

Infinite Solutions (the equation is always true)

Front

What is the first step to solve a linear equation?

Back

The first step is to isolate the variable on one side of the equation.

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.