# The blank in the statement “If x &lt; 5 , then x − 3 _ _ _ _ 2 .” with appropriate inequality sign.

### Precalculus: Mathematics for Calcu...

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

### 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 x−3____2.” with appropriate inequality sign.

Expert Solution

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 x≤5, then 3x____15.” with appropriate inequality sign.

Expert Solution

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 x≥2, then −3x____−6.” with appropriate inequality sign.

Expert Solution

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

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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