Understand and use equivalence

Which of the following expressions is equivalent to 2(x + 3)?

• 2x + 6

• 4 + 2x

• x + x

• 2x + 4

Answer explanation

To simplify 2(x + 3), distribute the 2: 2 * x + 2 * 3 = 2x + 6. Thus, the expression equivalent to 2(x + 3) is 2x + 6, making it the correct choice.

What is the equivalent expression for 3y + 2y?

• 3y + 3y

• y + y + y + y + y

• 5y

• 6y

Which of the following statements is true?

• 3 + 2 = 5

• 6 - 2 = 2 + 3

Simplify the expression 2x + 3x. What is the equivalent expression?

• 5x

• 3x + 2x

• 2x × 3x

What is the expression for total income generated by selling t tickets at £5 each?

• 5t

• t × 5

• 5 + t

• t + 5

Answer explanation

The total income from selling t tickets at £5 each is calculated by multiplying the number of tickets (t) by the price per ticket (£5). Thus, the correct expressions are 5t and t × 5.

If x + 5 = 10, which of the following is correct?

• x = 10 - 5

Is (5 - (3 + 2)) equivalent to (0)?

• No, because 3 + 2 = 6

• Yes, because 5 - 5 = 0

• No, it simplifies to 5

• Yes, it simplifies to 0

Which of the following is an equivalent expression for 3(a + 4)?

• 3a + 12

• a + 4 + a + 4 + a + 4

• 3a + 4

• 3 x a + 3 × 4

• It represents a multiplication operation

• It is used for addition only

• It shows that one expression is greater than the other

• It shows that two expressions are equal for all values of the variables

Which of the following is an example of two equivalent expressions?

• 2(x + 3) and 2x + 6

• x + x and 2x

• 3y + 2y and 5y

• x² and x + x