Flashcard 3.2

Front

What is the process to clear a fraction in an equation?

Back

To clear a fraction in an equation, multiply both sides of the equation by the least common denominator (LCD) of all the fractions present.

Front

What is the least common denominator (LCD) of the fractions \( \frac{5}{24} \) and \( \frac{1}{3} \)?

Back

The least common denominator (LCD) of \( \frac{5}{24} \) and \( \frac{1}{3} \) is 24.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation \( \frac{5}{24} + c = \frac{1}{3} \)?

Back

The first step is to clear the fraction by multiplying the entire equation by the least common denominator, which is 24.

Front

If \( c \) is isolated in the equation \( 15 + 72c = 24 \), what is the next step to solve for \( c \)?

Back

Subtract 15 from both sides to get \( 72c = 24 - 15 \), which simplifies to \( 72c = 9 \).

Front

What is the solution for \( c \) in the equation \( 72c = 9 \)?

Back

To solve for \( c \), divide both sides by 72, resulting in \( c = \frac{9}{72} = \frac{1}{8} \).

Front

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

Back

Clearing the fraction means eliminating the fractions from the equation to simplify the solving process.

Front

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

Back

The least common denominator allows you to eliminate fractions, making it easier to manipulate and solve the equation.

Front

How can you check your solution after solving for \( c \)?

Back

Substitute the value of \( c \) back into the original equation to verify that both sides are equal.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is \( Ax + By = C \), where A, B, and C are constants.