Q7. Solve for x: \( \frac{x}{a} - bx = c \)

Background

Topic: Solving Linear Equations for a Variable

This question tests your ability to manipulate algebraic equations to isolate a specific variable, a fundamental skill in College Algebra.

Key Terms and Formulas:

• Linear equation: An equation involving variables to the first power.

• Isolate: To get the variable alone on one side of the equation.

Step-by-Step Guidance

1. Start by identifying all terms containing \( x \) and move them to one side of the equation.

2. Factor \( x \) out of the terms where possible to simplify the equation.

3. Express the equation so that \( x \) is multiplied by a single coefficient.

4. Set up the equation to solve for \( x \) by dividing both sides by the coefficient of \( x \).

Try solving on your own before revealing the answer!

Q8. Solve for L: \( S = 2LW + 2LH + 2HW \)

Background

Topic: Solving Formulas for a Variable

This question tests your ability to rearrange a formula to solve for a specific variable, which is a common skill in College Algebra and applied mathematics.

Key Terms and Formulas:

• Formula: An equation that relates multiple variables.

• Isolate: To get the variable alone on one side of the equation.

Step-by-Step Guidance

1. Identify all terms containing \( L \) in the equation.

2. Group the terms with \( L \) together on one side of the equation.

3. Factor \( L \) out of the grouped terms.

4. Set up the equation so that \( L \) is multiplied by a single expression, then prepare to solve for \( L \).

Try solving on your own before revealing the answer!

Q9. Solve for c: \( \frac{1}{a} + \frac{1}{b} - \frac{1}{c} = d \)

Background

Topic: Solving Rational Equations for a Variable

This question tests your ability to manipulate rational equations and solve for a variable in the denominator, a key skill in College Algebra.

Key Terms and Formulas:

• Rational equation: An equation involving fractions with variables in the denominator.

• Isolate: To get the variable alone on one side of the equation.

Step-by-Step Guidance

1. Move the \( \frac{1}{c} \) term to one side of the equation and all other terms to the opposite side.

2. Express the equation so that \( \frac{1}{c} \) is isolated.

3. Take the reciprocal of both sides to solve for \( c \).

4. Set up the final expression for \( c \) in terms of the other variables.

Try solving on your own before revealing the answer!