Unit 3 Test

Front

What is the process to eliminate fractions in an equation?

Back

To eliminate fractions, multiply every term in the equation by the least common denominator (LCD) of all the fractions present.

Front

What is the least common denominator (LCD) of the fractions \( \frac{3}{2}x \) and \( \frac{4}{5} \)?

Back

The LCD of \( \frac{3}{2} \) and \( \frac{4}{5} \) is 10.

Front

How do you solve the equation \( 2 = \frac{3}{2}x + \frac{4}{5} \)?

Back

Multiply through by 10 to eliminate fractions: \( 20 = 15x + 8 \). Then isolate x.

Front

What is the first step in solving the equation \( 20 = 15x + 8 \)?

Back

Subtract 8 from both sides: \( 20 - 8 = 15x \) which simplifies to \( 12 = 15x \).

Front

How do you isolate x in the equation \( 12 = 15x \)?

Back

Divide both sides by 15: \( x = \frac{12}{15} = \frac{4}{5} \).

Front

What does it mean to 'clear the fraction' in an equation?

Back

Clearing the fraction means to eliminate the fractions by multiplying through by the least common denominator.

Front

What is the importance of the least common denominator in solving equations with fractions?

Back

The least common denominator allows you to simplify the equation by eliminating fractions, making it easier to solve.

Front

What is the general form of a linear equation?

Back

A linear equation is generally expressed as \( ax + b = c \), where a, b, and c are constants.

Front

What is the solution to the equation \( 20 = 15x + 8 \)?

Back

The solution is \( x = \frac{4}{5} \).

Front

What is the definition of a variable in algebra?

Back

A variable is a symbol, often represented by letters, that stands for a number that can change or vary.