Question 1

Which of the following is the correct first step to solve $$P = 2a + 2b$$ for $$b$$?

Accepted Answer

Subtract $$2a$$ from both sides.

Question 2

After subtracting $$2a$$ from both sides of $$P = 2a + 2b$$, what is the resulting equation?

Accepted Answer

$$P - 2a = 2b$$

Question 3

What is the final expression for $$b in $$terms of $$P$$ and $$a$$ after solving $$P = 2a + 2b$$?

Accepted Answer

$$b = \frac{P - 2a}{2}$$

Question 4

Which property is used when subtracting $$2a$$ from both sides of the equation $$P = 2a + 2b$$?

Accepted Answer

Addition property of equality

Question 5

If $$P = 18$$ and $$a = 4$$, what is the value of $$b in$$ $$P = 2a + 2b$$?

Accepted Answer

$$b = 5$$

Question 6

Which of the following is an equivalent form of $$b = \frac{P - 2a}{2}$$?

Accepted Answer

$$b = \frac{P}{2} - a$$

Question 7

Which step is NOT necessary when solving $$P = 2a + 2b$$ for $$b$$?

Accepted Answer

Multiplying both sides by the least common denominator

Question 8

If $$P = 2a + 2b$$ represents the perimeter of a rectangle, what do $$a$$ and $$b$$ represent?

Accepted Answer

The length and the width

Question 9

Which property is used when dividing both sides of $$P - 2a = 2b by$$ $$2$$?

Accepted Answer

Multiplication property of equality

Question 10

A chemist uses the formula $$P = 2a + 2b to $$calculate the perimeter of a rectangular lab table. If the perimeter is $$30$$ meters and the length is $$8$$ meters, what is the width?

Accepted Answer

$$b = 7$$ meters

Question 11

Which of the following best describes the process of isolating $$b in$$ $$P = 2a + 2b$$?

Accepted Answer

Move all terms with $$b to $$one side, then divide by the coefficient of $$b.$$

Question 12

If $$P = 2a + 2b$$ and $$a = 0$$, what is $$b in $$terms of $$P$$?

Accepted Answer

$$b = \frac{P}{2}$$

Question 13

Which of the following is a common mistake when solving $$P = 2a + 2b$$ for $$b$$?

Accepted Answer

Dividing $$P by$$ $$2$$ before subtracting $$2a$$

Question 14

If $$P = 2a + 2b$$ and $$b = 3$$, $$a = 5$$, what is $$P$$?

Accepted Answer

$$P = 16$$

Question 15

Which step would you use if the equation had fractions, such as $$P = \frac{2a}{3} + 2b$$?

Accepted Answer

Multiply both sides by the least common denominator

Solving Equations for a Specified Variable: Step-by-Step Guide

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