Asked by .

Solve for xx and graph the solution on the number line below.3, is greater than or equal to, x, minus, 53≥x−5
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Solve for xx and graph the solution on the number line below.
minus, 4, is greater than or equal to, x, minus, 11
−4≥
x−11
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Solve for xx and graph the solution on the number line below.
minus, 1, is less than, start fraction, x, divided by, 2, end fraction
−1<
2
x
​
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Solve for xx and graph the solution on the number line below.
minus, 7, x, is less than or equal to, 7
−7x≤
7
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Solve the inequality and graph the solution on the line provided.
minus, 16, plus, 5, x, is less than, minus, 26
−16+5x<
−26
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Solve the inequality and graph the solution on the line provided.
minus, 5, x, plus, 8, is greater than, 3
−5x+8>
3
Answer
Answered by .
Which of the following values are solutions to the inequality minus, 8, is less than, 2, x, plus, 2, question mark−8<2x+2?
I., minus, 5, II., minus, 10, III., minus, 4
I.−5II.−10III.−4
Answered by .
Alonso has a points card for a movie theater.
He receives 40 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 185 points for a free movie ticket.

Write and solve an inequality which can be used to determine xx, the number of visits Alonso can make to earn his first free movie ticket.
Answered by GPT 3.5
To solve the inequality 3 ≥ x - 5, we can add 5 to both sides to isolate x:
3 + 5 ≥ x - 5 + 5
8 ≥ x

Therefore, the solution to the inequality is x ≤ 8.

Graphing this solution on the number line:
Answered by GPT 3.5
To solve the inequality -4 ≥ x - 11, we can add 11 to both sides to isolate x:
-4 + 11 ≥ x - 11 + 11
7 ≥ x

Therefore, the solution to the inequality is x ≤ 7.

Graphing this solution on the number line:
Answered by GPT 3.5
To solve the inequality -1 < (x/2), we can multiply both sides by 2 to remove the fraction:
2 * -1 < 2 * (x/2)
-2 < x

Therefore, the solution to the inequality is x > -2.

Graphing this solution on the number line:
Answered by GPT 3.5
To solve the inequality -7x ≤ 7, we can divide both sides by -7. However, when dividing by a negative number, the direction of the inequality sign must be reversed:
(-7x)/(-7) ≥ 7/(-7)
x ≥ -1

Therefore, the solution to the inequality is x ≥ -1.

Graphing this solution on the number line:
Answered by GPT 3.5
To solve the inequality -16 + 5x < -26, we need to isolate the variable x.

First, we can add 16 to both sides of the inequality:
-16 + 5x + 16 < -26 + 16
5x < -10

Next, divide both sides of the inequality by 5 (since the coefficient of x is 5):
(5x)/5 < (-10)/5
x < -2

Therefore, the solution to the inequality is x < -2.

Graphing this solution on the number line:
Answered by GPT 3.5
To solve the inequality -5x + 8 > 3, we need to isolate the variable x.

First, we can subtract 8 from both sides of the inequality:
-5x + 8 - 8 > 3 - 8
-5x > -5

Next, divide both sides of the inequality by -5. Remember that when dividing by a negative number, the direction of the inequality sign must be reversed:
(-5x)/(-5) < (-5)/(-5)
x < 1

Therefore, the solution to the inequality is x < 1.

Graphing this solution on the number line:
Answered by GPT 3.5
To determine which of the given values are solutions to the inequality -8 < 2x + 2, we can substitute each value into the inequality and see if it holds true.

I. -5
-8 < 2(-5) + 2
-8 < -10 + 2
-8 < -8 (True)

II. -10
-8 < 2(-10) + 2
-8 < -20 + 2
-8 < -18 (True)

III. -4
-8 < 2(-4) + 2
-8 < -8 + 2
-8 < -6 (False)

Therefore, the values that are solutions to the inequality are I. -5 and II. -10.
Answered by GPT 3.5
Let x represent the number of visits Alonso can make to earn his first free movie ticket.

Alonso earns 12.5 points for each visit to the movie theater. So, the total number of points earned from his visits would be 12.5x.

Considering that Alonso received 40 points just for signing up, the total number of points Alonso will have is 12.5x + 40.

We want to find the minimum value of x that will result in a total number of points greater than or equal to 185, which is the number of points needed for a free movie ticket.

Therefore, we can write the following inequality:
12.5x + 40 ≥ 185

To solve this inequality, we can subtract 40 from both sides:
12.5x ≥ 185 - 40
12.5x ≥ 145

Finally, we divide both sides by 12.5 to solve for x:
x ≥ 145 / 12.5
x ≥ 11.6

Since the value of x must be a whole number (as you cannot have a fraction of a visit), we round up to the nearest whole number.

Therefore, Alonso must make at least 12 visits to earn his first free movie ticket.