Chapter 3.4, Problem 25P

Reasoning a. Solve $3v-5\le 2v+10$ by gathering the variable terms on the left side and the constant terms on the right side of the inequality.

b. Solve $3v-5\le 2v+10$ by gathering the constant terms on the left side and the variable terms on the right side of the inequality.

c. Compare the results of parts (a) and (b).

d. Which method do you prefer? Explain.

To determine

To calculate: Gather variable terms on left side and constant terms on the right side of the inequality.

Answer to Problem 25P

  $v\le 15$

Explanation of Solution

Given information: The inequality $3v-5\le 2v+10$

Calculation:

Let’s gather variable terms on the left side by subtracting both sides 2v.

It gives $v-5\le 10$

Add both sides 5

  $v\le 15$

To determine

To calculate: Bring all variable terms to the right side of the inequality and constants to the left side of the equation.

Answer to Problem 25P

  $v\le 15$

Explanation of Solution

Given information: The inequality $3v-5\le 2v+10$

Calculation:

  $3v-5\le 2v+10$

Subtract both sides 3v

  $-5\le -v+10$

Subtract both sides 10.

  $-15\le -v$

Divide both sides by -1.

  $15\ge v$

It can be rewritten as

  $v\le 15$

To determine

To find: The method do you prefer part A or partB?

Answer to Problem 25P

I would prefer the method the part A is used because we could solve the inequality within few steps.

Explanation of Solution

Both give the same answer in part A and part B.

To determine

To find: The method do you prefer?

Answer to Problem 25P

I would prefer the method the part A is used because we could solve the inequality within few steps.

Explanation of Solution

Even though both methods gives us same answer first way is simple, easy and less steps are needed.