Algebra 1 Midterm Review

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean for an equation to have one solution?

Back

An equation has one solution when there is exactly one value for the variable that makes the equation true.

Front

What does it mean for an equation to have no solutions?

Back

An equation has no solutions when there is no value for the variable that can satisfy the equation.

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when any value for the variable makes the equation true, often resulting from identical expressions on both sides.

Front

How do you simplify the equation 5x + 6 = 2 + 3x?

Back

Subtract 3x from both sides: 2x + 6 = 2. Then subtract 6: 2x = -4. Divide by 2: x = -2. The equation has one solution.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

How do you simplify the equation 3x - 7 = 3(x - 3) + 2?

Back

Distribute: 3x - 7 = 3x - 9 + 2. Combine like terms: 3x - 7 = 3x - 7. This results in an identity, meaning infinite solutions.

Front

How do you simplify the equation 3x - 8 = 3(x - 4) + 1?

Back

Distribute: 3x - 8 = 3x - 12 + 1. Combine like terms: 3x - 8 = 3x - 11. This results in no solutions.

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 and graphs as a straight line.