Question 1

6H + H - 20 = 44 - H; H = 8.

Accepted Answer

Simplify the equation by combining like terms:

6H + H + 20 = 44 - H + 20
7H + 20 = 64 - H
8H = 44
H = 8

Therefore, the statement "H = 8" is true, making the answer A.

Question 2

Whatever you do to one side of an equation, you must do to the other.

Accepted Answer

This is known as the "golden rule" of solving equations. It ensures that the equation stays balanced and maintains its equality.

Question 3

An equation represents a math expression of equality.

Accepted Answer

An equation shows that two expressions are equal.

Question 4

Variables can only be numbers.

Accepted Answer

Variables can hold different types of data including numbers, strings, and objects.

Question 5

B + 8 = 9; B = 17.

Accepted Answer

If B + 8 = 9, then subtracting 8 from both sides gives B = 1, not 17.

Question 6

2(V- 8) = 90; V = 53.

Accepted Answer

Substitute V = 53 into the equation:

2(53-8) = 90

2(45) = 90

90 = 90

Therefore, the equation is true when V = 53.

Question 7

In word problems, the word "of" indicates an equal sign.

Accepted Answer

The word "of" does not always indicate an equal sign in word problems. It can indicate multiplication, division, or part-whole relationships. It is important to carefully read and interpret the entire problem to determine the correct mathematical operation.

Question 8

B/5 + 3 = 15; B = 16.

Accepted Answer

To solve for B, we need to isolate it on one side of the equation.

First, we can subtract 3 from both sides:

B/5 + 3 - 3 = 15 - 3

Simplifying:

B/5 = 12

To solve for B, we can multiply both sides by 5:

5 * (B/5) = 5 * 12

Simplifying:

B = 60

Therefore, the statement "B = 16" is false.

Question 9

There is only one set way to solve all word problems.

Accepted Answer

There are often multiple ways to approach and solve a word problem, and sometimes there may be more than one correct answer. It is important to understand the problem and choose a method that makes sense for each individual situation.

Question 10

20(C - 9) means the 20 is multiplied only times the C to clear the parentheses.

Accepted Answer

The expression 20(C - 9) means 20 is multiplied by the entire quantity (C - 9), not just C.

Question 11

More than one unknown in a word problem can be represented in terms of the same variable assigned to first unknown.

Accepted Answer

This is true. Often in word problems, multiple unknowns are related and can be expressed in terms of each other using the same variable.

Question 12

4C stands for twice Cathy's age.

Accepted Answer

The statement doesn't specify what 4C is referring to, so it cannot be determined that it stands for twice Cathy's age.

Question 13

4 + 3 = 9 is an equation of equality.

Accepted Answer

4 + 3 = 7, not 9. Therefore, 4 + 3 = 9 is not an equation of equality.

Question 14

When an equation uses addition, the variable can be solved by the opposite process: subtraction.

Accepted Answer

When you subtract the same number from each side of an equation that uses addition, you can isolate the variable and solve it.

Question 15

Variables and constants are terms of mathematical expressions.

Accepted Answer

Variables and constants are terms used in mathematical expressions.

Question 16

No number in front of a letter is really a 1.

Accepted Answer

This statement is true, as no number in front of a letter represents a 1, unless it is explicitly written as such. For example, A1 would indicate the first column in a spreadsheet, whereas A10 would indicate the tenth column.

Question 17

B - 11 = 40; B = 29.

Accepted Answer

The answer of B - 11 = 40; B =...

Question 18

B/30 = 9; B = 270.

Accepted Answer

This is true because if you multiply both sides of the equation B/30 = 9 by 30, you get B = 270.

Question 19

A formula is not an equation.

Accepted Answer

The answer of A formula is not an equation....

Question 20

B - 6 represents Bob's age six years ago.

Accepted Answer

The expression "B ? 6" suggests an operation involving B (Bob's age) and 6, which, when properly interpreted (e.g., B - 6), would represent Bob's age six years ago.

Quiz 5: Solving for the Unknown: a How-To Approach for Solving Equations