Q1. Determine if the following is an expression or an equation: 5x + 3 = 8

Background

Topic: Expressions vs. Equations

This question tests your understanding of the difference between mathematical expressions and equations.

Key Terms:

• Expression: A mathematical phrase that can contain numbers, variables, and operations, but does not have an equals sign.

• Equation: A mathematical statement that shows two expressions are equal, using an equals sign (=).

Step-by-Step Guidance

1. Look for an equals sign (=) in the given statement.

2. If there is an equals sign, it is an equation. If not, it is an expression.

3. Examine the given statement: .

Try solving on your own before revealing the answer!

Q2. Determine which of the following equations are linear equations in one variable, x:

Background

Topic: Linear Equations

This question tests your ability to identify linear equations in one variable.

Key Terms:

• Linear Equation: An equation where the variable has a degree of 1 and appears in the form .

• One Variable: Only the variable is present.

Step-by-Step Guidance

1. Check each equation to see if is raised to the first power (not squared, cubed, etc.).

2. Make sure there are no other variables besides .

3. Look for equations in the form .

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Q3. Solve the following equations:

Background

Topic: Solving Linear Equations

This question tests your ability to solve for in linear equations.

Key Formula:

• To solve , isolate by performing inverse operations.

Step-by-Step Guidance

1. Identify the equation you need to solve, such as .

2. Add or subtract to isolate the term with .

3. Divide or multiply to solve for .

4. Check your solution by plugging it back into the original equation.

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Q4. Find the value of so that the angles are supplementary.

Background

Topic: Supplementary Angles

This question tests your understanding of supplementary angles and how to set up an equation to solve for .

Key Terms and Formula:

• Supplementary Angles: Two angles whose measures add up to .

• Set up the equation:

Step-by-Step Guidance

1. Write the equation: .

2. Substitute the expressions for the angles given in the problem.

3. Solve for using algebraic methods.

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Q5. The perimeter of a rectangle is 280 ft. The length is 2x more than twice the width. Find the length and width.

Background

Topic: Perimeter of Rectangles & Linear Equations

This question tests your ability to set up and solve equations based on geometric relationships.

Key Formula:

• Perimeter of a rectangle:

• Length in terms of width:

Step-by-Step Guidance

1. Write the perimeter equation: .

2. Substitute the expression for in terms of .

3. Solve for using algebraic methods.

4. Once you have , substitute back to find .

Try solving on your own before revealing the answer!