Topic 4 Practice Quiz: Understanding Expressions and Equations

Answer explanation

To simplify 3(x + 4), distribute 3: 3 * x + 3 * 4 = 3x + 12. Thus, the expression equivalent to 3(x + 4) is 3x + 12, making it the correct choice.

Answer explanation

To solve the equation x + 5 = 12, subtract 5 from both sides: x = 12 - 5. This simplifies to x = 7, which is the correct answer.

Answer explanation

To find the value of y when x = 4, substitute 4 into the equation y = 3x + 2: y = 3(4) + 2 = 12 + 2 = 14. Thus, the correct answer is y = 14.

Answer explanation

The statement "A number x is greater than 7" translates to the inequality x > 7. This means x must be any value larger than 7, making the correct choice x > 7.

Answer explanation

To simplify 2(3x + 5), distribute the 2: 2 * 3x + 2 * 5 = 6x + 10. Thus, the equivalent expression is 6x + 10, which is the correct choice.

Answer explanation

To solve the equation 4x = 20, divide both sides by 4. This gives x = 20 / 4, which simplifies to x = 5. Therefore, the correct answer is x = 5.

Answer explanation

Let the number of oranges be represented by \(o\). Since there are 5 more apples than oranges, the number of apples is \(o + 5\). Thus, the correct choice is \(o + 5\).

Answer explanation

To find the value of y when x = 5, substitute 5 into the equation y = 2x - 3: y = 2(5) - 3 = 10 - 3 = 7. Thus, the correct answer is y = 7.

Answer explanation

The statement "A number x is less than 10" directly translates to the inequality x < 10. This means x must be any value smaller than 10, making the correct choice x < 10.

Answer explanation

To simplify the expression 5(x + 2) - 3x, distribute 5 to get 5x + 10, then subtract 3x to get 2x + 10. Thus, the equivalent expression is 2x + 10.