BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.7, Problem 1E

(a)

To determine

To fill: The blank in the statement “If x<5, then x3____2.” with appropriate inequality sign.

Expert Solution

Answer to Problem 1E

The complete statement is “If x<5, then x3<2_”.

Explanation of Solution

Rule used:

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

That is, if AB, then ACBC, where A, B and C are real numbers or algebraic expressions.

Calculation:

Consider the given inequality x<5.

The left-hand side of the resulting inequality is given as x3.

Therefore, subtract the same number 3, from both sides of the given inequality x<5.

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

x<5x3<53x3<2

Thus, the complete statement is “If x<5, then x3<2_”.

(b)

To determine

To fill: The blank in the statement “If x5, then 3x____15.” with appropriate inequality sign.

Expert Solution

Answer to Problem 1E

The complete statement is “If x5, then 3x15_”.

Explanation of Solution

Rule used:

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

That is, if AB, then CACB, where A, B and C are real numbers or algebraic expressions and C>0.

Calculation:

Consider the given inequality x5.

The left-hand side of the resulting inequality is given as 3x.

Therefore, multiply both sides of the given inequality x5 by 3.

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

x53x353x15

Thus, the complete statement is “If x5, then 3x15_”.

(c)

To determine

To fill: The blank in the statement “If x2, then 3x____6.” with appropriate inequality sign.

Expert Solution

Answer to Problem 1E

The complete statement is “If x2, then 3x6_”.

Explanation of Solution

Rule used:

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

That is, if AB, then CACB, where A, B and C are real numbers or algebraic expressions and C<0.

Calculation:

Consider the given inequality x2.

The left-hand side of the resulting inequality is given as 3x.

Therefore, multiply the same number 3, on both sides of the given inequality x2.

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

x23x323x6

Thus, the complete statement is “If x2, then 3x6_”.

(d)

To determine

To fill: The blank in the statement “If x<2, then x____2.” with appropriate inequality sign.

Expert Solution

Answer to Problem 1E

The complete statement is “If x<2, then x>2_”.

Explanation of Solution

Consider the given inequality x<2.

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

Therefore, multiply the same number 1, on the both sides of the given inequality x<2.

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

x<21x>12x>2

Thus, the complete statement is “If x<2, then x>2_”.

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