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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.7, Problem 1E

(**a**)

To determine

**To fill:** The blank in the statement “If

Expert Solution

The complete statement is “If

**Rule used:**

Subtracting the same quantity from each side of an inequality gives an equivalent inequality.

That is, if *A*, *B* and *C* are real numbers or algebraic expressions.

**Calculation:**

Consider the given inequality

The left-hand side of the resulting inequality is given as

Therefore, subtract the same number 3, from both sides of the given inequality

Then, by the rule stated above, the inequality becomes as follows.

Thus, the complete statement is “If

(**b**)

To determine

**To fill:** The blank in the statement “If

Expert Solution

The complete statement is “If

**Rule used:**

Multiplying each side of an inequality by the same positive quantity gives an equivalent inequality.

That is, if *A*, *B* and *C* are real numbers or algebraic expressions and

**Calculation:**

Consider the given inequality

The left-hand side of the resulting inequality is given as

Therefore, multiply both sides of the given inequality

Then, by the rule stated above, the inequality becomes as follows.

Thus, the complete statement is “If

(**c**)

To determine

**To fill:** The blank in the statement “If

Expert Solution

The complete statement is “If

**Rule used:**

Multiplying each side of an inequality by the same negative quantity reverses the direction of the inequality.

That is, if *A*, *B* and *C* are real numbers or algebraic expressions and

**Calculation:**

Consider the given inequality

The left-hand side of the resulting inequality is given as

Therefore, multiply the same number

Then, by the rule stated above, the inequality becomes as follows.

Thus, the complete statement is “If

(**d**)

To determine

**To fill:** The blank in the statement “If

Expert Solution

The complete statement is “If

Consider the given inequality

The left-hand side of the resulting inequality is given as

Therefore, multiply the same number

Then, by the rule stated in part (**c**), the inequality becomes as follows.

Thus, the complete statement is “If