Question

Solve the inequality.

2 left-parenthesis m minus 3 right-parenthesis plus 7 less than 21

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality:

2(m - 3) + 7 < 21

First distribute 2 to both terms inside parentheses:

2m - 6 + 7 < 21

Combine like terms:

2m + 1 < 21

Subtract 1 from both sides:

2m + 1 - 1 < 21 - 1

2m < 20

Divide both sides by 2:

(2m)/2 < 20/2

m < 10

Thus, the solution to the inequality is m < 10.

Answer 2

Solve the inequality.

negative 2 left-parenthesis w plus 4 right-parenthesis plus 9 less than negative 11

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the inequality:

-2(w + 4) + 9 < -11

First distribute -2 to both terms inside parentheses:

-2w - 8 + 9 < -11

Combine like terms:

-2w + 1 < -11

Subtract 1 from both sides:

-2w + 1 - 1 < -11 - 1

-2w < -12

Divide both sides by -2, remember to reverse the inequality when dividing by a negative number:

(-2w) / -2 > (-12) / -2

w > 6

Thus, the solution to the inequality is w > 6.

Answer 4

The lengths of the sides of a triangle are in the ratio 5 colon 6 colon 7. Describe the length of the longest side if the perimeter is less than 54 cm.

Answer 5

[AI-generated answer — Bot GPT 3.5]

Let's assume that the common ratio for the sides of the triangle is "x".

According to the given information, the lengths of the sides are 5x, 6x, and 7x.

The perimeter of the triangle is the sum of the lengths of all three sides:

Perimeter = 5x + 6x + 7x = 18x

We're given that the perimeter is less than 54 cm:

18x < 54

Divide both sides of the inequality by 18:

x < 3

Since x represents the common ratio, it needs to be a positive number. The largest positive integer less than 3 is 2.

So, x = 2.

Therefore, the lengths of the sides of the triangle are 5x = 5 * 2 = 10 cm, 6x = 6 * 2 = 12 cm, and 7x = 7 * 2 = 14 cm.

Among these lengths, the longest side is 14 cm.

Answer 6

Find the lesser of two consecutive integers with a sum greater than 16.

Answer 7

[AI-generated answer — Bot GPT 3.5]

Let's assume the two consecutive integers are x and x+1.

According to the given information, the sum of these integers is greater than 16:

x + (x+1) > 16

Combine like terms:

2x + 1 > 16

Subtract 1 from both sides:

2x > 15

Divide both sides by 2:

x > 7.5

Since we need to find the lesser of the two consecutive integers, we consider the integer value less than 7.5, which is 7.

Therefore, the lesser of the two consecutive integers with a sum greater than 16 is 7.

Answer 8

Find the lesser of two consecutive integers with a sum greater than 16.

(2 points)
Responses

The lesser number is greater than or equal to 8.
The lesser number is greater than or equal to 8.

The lesser number is greater than or equal to 12.
The lesser number is greater than or equal to 12.

The lesser number is greater than or equal to 7.
The lesser number is greater than or equal to 7.

The lesser number is greater than or equal to 14.

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let's assume the two consecutive integers are x and x+1.

According to the given information, the sum of these integers is greater than 16:

x + (x+1) > 16

Combine like terms:

2x + 1 > 16

Subtract 1 from both sides:

2x > 15

Divide both sides by 2:

x > 7.5

Since we are looking for the lesser of the two consecutive integers, we consider the integer value that is greater than 7.5, which is 8.

Therefore, the lesser of the two consecutive integers with a sum greater than 16 is 8.

Answer 10

[AI-generated answer — Explain Bot]

To solve the inequality, we need to isolate the variable m.

We have:

2(m - 3) + 7 < 21

Let's begin by simplifying the expression within the parentheses:

2m - 6 + 7 < 21

Next, we combine like terms:

2m + 1 < 21

To isolate the variable m, we subtract 1 from both sides of the inequality:

2m < 20

Finally, we divide both sides of the inequality by 2 to solve for m:

m < 10

Therefore, the solution to the inequality is m < 10.