Math / Algebra

Question19. Sana says, "I know that 5 is greater than 4.5. Therefore, -5 must be greater than -4.5 ". Is Sana correct? Explain.
Remember

Studdy Solution

STEP 1

1. Sana is comparing positive and negative numbers.
2. We need to determine if Sana's statement about negative numbers is correct.

STEP 2

1. Understand the properties of inequalities.
2. Apply these properties to the given numbers.
3. Determine if Sana's conclusion is correct.

STEP 3

Understand that if $a > b$ , then for positive numbers, $a$ is indeed greater than $b$ .

STEP 4

For negative numbers, if $a > b$ , then $-a < -b$ . This is because multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

STEP 5

Given $5 > 4.5$ , when we take the negative of both sides, we have $-5 < -4.5$ .
Sana's statement is incorrect. The correct inequality is:
$-5 < -4.5$

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Question19. Sana says, "I know that 5 is greater than 4.5. Therefore, -5 must be greater than -4.5 ". Is Sana correct? Explain.
Remember

Studdy Solution

STEP 1

1. Sana is comparing positive and negative numbers.
2. We need to determine if Sana's statement about negative numbers is correct.

STEP 2

1. Understand the properties of inequalities.
2. Apply these properties to the given numbers.
3. Determine if Sana's conclusion is correct.

STEP 3

Understand that if $a > b$ , then for positive numbers, $a$ is indeed greater than $b$ .

STEP 4

For negative numbers, if $a > b$ , then $-a < -b$ . This is because multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

STEP 5

Given $5 > 4.5$ , when we take the negative of both sides, we have $-5 < -4.5$ .
Sana's statement is incorrect. The correct inequality is:
$-5 < -4.5$

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Question19. Sana says, "I know that 5 is greater than 4.5. Therefore, -5 must be greater than -4.5 ". Is Sana correct? Explain.Remember

Studdy Solution

STEP 1

1. Sana is comparing positive and negative numbers.2. We need to determine if Sana's statement about negative numbers is correct.

STEP 2

1. Understand the properties of inequalities.2. Apply these properties to the given numbers.3. Determine if Sana's conclusion is correct.

STEP 3

Understand that if a>b a > b a>b, then for positive numbers, a a a is indeed greater than b b b.

STEP 4

For negative numbers, if a>b a > b a>b, then −a<−b-a < -b−a<−b. This is because multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

STEP 5

Given 5>4.5 5 > 4.5 5>4.5, when we take the negative of both sides, we have −5<−4.5-5 < -4.5−5<−4.5. Sana's statement is incorrect. The correct inequality is:−5<−4.5 -5 < -4.5 −5<−4.5

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question19. Sana says, "I know that 5 is greater than 4.5. Therefore, -5 must be greater than -4.5 ". Is Sana correct? Explain.
Remember

1. Sana is comparing positive and negative numbers.
2. We need to determine if Sana's statement about negative numbers is correct.

1. Understand the properties of inequalities.
2. Apply these properties to the given numbers.
3. Determine if Sana's conclusion is correct.

Understand that if $a > b$ , then for positive numbers, $a$ is indeed greater than $b$ .

For negative numbers, if $a > b$ , then $-a < -b$ . This is because multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

Given $5 > 4.5$ , when we take the negative of both sides, we have $-5 < -4.5$ .
Sana's statement is incorrect. The correct inequality is:
$-5 < -4.5$