Q1. Simplify the following expressions and determine whether the given statement is true or false:

• 3(5 + 2) > 3(5) + 2

• 10 - 2 > 8 + 3 - 1

• 15 - 2(4 + 3) = 1

Background

Topic: Order of Operations and Properties of Equality/Inequality

This question tests your understanding of the order of operations (PEMDAS/BODMAS) and how to evaluate and compare algebraic expressions.

Key Terms and Formulas

• Order of Operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

• Properties of Equality and Inequality

Step-by-Step Guidance

1. For each expression, start by simplifying inside the parentheses.

2. Apply multiplication or division as indicated.

3. Perform addition or subtraction as the last step.

4. Compare the simplified results to determine if the statement is true or false.

5. For inequalities, check if the left side is greater than the right side after simplification.

Try solving on your own before revealing the answer!

Q2. Simplify the following algebraic expressions:

• a)

• b)

• c)

• d)

• e)

• f)

• g)

• h)

• i)

• j)

• k)

• l)

Background

Topic: Combining Like Terms

This question tests your ability to combine like terms in algebraic expressions, which is a foundational skill in algebra.

Key Terms and Formulas

• Like Terms: Terms that have the same variable(s) raised to the same power(s).

• Combining Like Terms: Add or subtract the coefficients of like terms.

Step-by-Step Guidance

1. Identify like terms in each expression (same variable and exponent).

2. Add or subtract the coefficients of the like terms.

3. Write the simplified expression using the combined coefficient and variable.

4. For expressions with more than one variable, group and combine each set of like terms separately.

Try solving on your own before revealing the answer!

Q3. Write an algebraic expression for each phrase, then simplify if possible:

• a) The sum of a number and 8

• b) The product of 4 and a number

• c) The difference of 12 and a number

• d) The quotient of a number and 3

• e) 3 less than twice a number

• f) 5 more than the product of 6 and a number

Background

Topic: Translating Verbal Phrases into Algebraic Expressions

This question tests your ability to convert word phrases into algebraic expressions, a key skill in algebra problem-solving.

Key Terms and Formulas

• Sum: Addition

• Product: Multiplication

• Difference: Subtraction

• Quotient: Division

• "Less than": Subtract from the following value

• "More than": Add to the following value

Step-by-Step Guidance

1. Identify the operation indicated by the phrase (sum, product, difference, quotient).

2. Let the variable represent "a number."

3. Translate each phrase into an algebraic expression using .

4. Simplify the expression if possible (e.g., combine like terms or write in standard form).

Try solving on your own before revealing the answer!

Q4. Write each phrase as an algebraic expression using x as the variable, and simplify:

• a) The sum of three times a number, nine times a number, eight times a number, and six times a number

• b) The sum of three times a number, nine times a number, and two times a number

• c) Five times a number added to the sum of the number and 3

• d) A number multiplied by 4, subtracted from the sum of six and eight times the number

• e) Nine times a number subtracted from the sum of six and eight times the number

• f) Six times a number subtracted from the sum of eight and nine times the number

Background

Topic: Translating and Simplifying Algebraic Expressions

This question tests your ability to translate complex verbal phrases into algebraic expressions and then simplify them by combining like terms.

Key Terms and Formulas

• Sum: Addition

• Product: Multiplication

• "Subtracted from": Reverse the order of subtraction

• Combine like terms to simplify

Step-by-Step Guidance

1. Assign as the variable representing "a number."

2. Translate each phrase into an algebraic expression using and the indicated operations.

3. For sums, add all the terms together; for "subtracted from," reverse the order of subtraction.

4. Combine like terms to write the expression in its simplest form.

Try solving on your own before revealing the answer!