Asked by Mr. Bombastic

Choose the missing step in the given solution to the inequality −x − 10 > 14 + 2x.

−x − 10 > 14 + 2x
−3x − 10 > 14
_____________
x < −8

−3x > 24
−3x > 4
−3x > −4
−3x < 24
Answered by Mr. Bombastic
Two boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats. The equation 4(x + 1) = 4x + 4 models the paths of the boats. Solve for x.

No solution
0
All real numbers
1
Answered by Mr. Bombastic
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle. Can the perimeter of the rectangle be 60 units when its width is 11 units and its length is 24 units?

No. If the length is 24 units and the width is 11 units, the perimeter would be P = 48 + 22 = 70 units, not 60.
No. If the length is 24 units and the width is 11 units, the perimeter would be P = 24 + 22 = 66 units, not 60.
Yes. If the perimeter is 60 units and the width is 11 units, then P + W is greater than 48.
Yes. If the length is 24 units and the width is 11 units, then P = 2L + 2W = 60
Answered by Mr. Bombastic
Zoya has to earn at least $300 to meet her fundraising goal. She has only 100 bracelets that she plans to sell at $5 each. Which inequality shows the number of bracelets, x, Zoya can sell to meet her goal?

60 ≤ x ≤ 100
60 ≤ x ≤ 300
100 ≤ x ≤ 300
20 ≤ x ≤ 100
Answered by Mr. Bombastic
Solve for x: −6 < x − 1 < 9

5 < x < 10
−5 < x < 10
−5 > x > 10
5 > x > −10
Answered by Bot
Add 2x to both sides:

-x - 10 + 2x > 14

Simplify:

x - 10 > 14

Add 10 to both sides:

x > 24

The missing step is:

Divide both sides by -1 and flip the inequality symbol:

x < -24
Answered by Bot
We can simplify the equation:

4(x + 1) = 4x + 4

Distribute the 4:

4x + 4 = 4x + 4

Simplify:

4 = 4

This equation is true for all values of x. Therefore, the solution is:

All real numbers.
Answered by Bot
No. If the length is 24 units and the width is 11 units, the perimeter would be P = 2(24) + 2(11) = 48 + 22 = 70 units, not 60.
Answered by Bot
Zoya plans to sell each bracelet at $5, so the total amount she would earn by selling x bracelets would be 5x.

To meet her goal, she has to earn at least $300:

5x ≥ 300

Divide both sides by 5:

x ≥ 60

Therefore, Zoya has to sell at least 60 bracelets to meet her goal.

The correct answer is:

60 ≤ x ≤ 100 (since she only has 100 bracelets to sell).
Answered by Bot
Add 1 to all parts of the inequality:

-6 + 1 < x - 1 + 1 < 9 + 1

Simplify:

-5 < x < 10

The correct answer is:

-5 < x < 10.