Determine the solution set of 2x>−8 and −5x+7=12 .(1 point)

Question

Responses

{x|x>−1}
left brace x vertical bar x greater than negative 1 right brace

{−4}
left brace negative 4 right brace

{x|x>−4}
left brace x vertical bar x greater than negative 4 right brace

{−1}

Determine the solution set of −3x+7=10 or 3x−9=0 .(1 point)
Responses

{3}
left brace 3 right brace

{−1,3}
left brace negative 1 comma 3 right brace

The solution set is null.
The solution set is null.

{−1}
left brace negative 1 right brace

Use the image to answer the question.

A number line ranges from negative 5 to 5 in increments of 1. An open point is plotted at 3, with a solid line extending right, beyond 5. An open point is plotted at negative 3, with a solid line extending left, beyond negative 5.

What solution set does the number line graph?

(1 point)
Responses

x<−3 and x>3
x less than negative 3 and x greater than 3

x≤−3 and x≥−3
x less-than-or-equal-to negative 3 and x greater-than-or-equal-to negative 3

x≤−3 or x≥−3
x less-than-or-equal-to negative 3 or x greater-than-or-equal-to negative 3

x<−3 or x>3

Use the image to answer the question.

A number line ranges from negative 10 to 2 in increments of 1. Two open points are plotted at negative 8 and negative 2, with a solid line extending between them.

Select the solution set represented on the graph.

(1 point)
Responses

x≥−8 or x≤−2
x greater-than-or-equal-to negative 8 or x less-than-or-equal-to negative 2

x≥−8 and x≤−2
x greater-than-or-equal-to negative 8 and x less-than-or-equal-to negative 2

x>−8 and x<−2
x greater than negative 8 and x less than negative 2

x>−8 or x<−2

Use the image to answer the question.

A number line ranges from 1 to 13 in increments of 1. A closed point is plotted at 10, with a solid line extending right, beyond 13. A closed point is plotted at 9, with a solid line extending left, beyond 1.

Select the solution set represented on the graph.

(1 point)
Responses

m>10 and m<9
m greater than 10 and m less than 9

m>10 or m<9
m greater than 10 or m less than 9

m≥10 or m≤9
m greater-than-or-equal-to 10 or m less-than-or-equal-to 9

m≥10 and m≤9...

Answer 1

Here are the correct responses for each of the problems presented:

1. For the inequalities: 2x > -8 and −5x + 7 = 12

   • Solve 2x > -8: Divide both sides by 2, leading to x > -4.
   • Solve −5x + 7 = 12: Subtract 7 from both sides to get −5x = 5, then divide by -5, leading to x = -1.
   • Therefore, the solution set in this context is {x | x > -4}, so the correct response is:
     • {x | x > −4}

2. For the equations: −3x + 7 = 10 or 3x − 9 = 0

   • Solve −3x + 7 = 10: Subtract 7 from both sides to get −3x = 3, then divide by -3, yielding x = -1.
   • Solve 3x − 9 = 0: Add 9 to both sides to get 3x = 9, then divide by 3, yielding x = 3.
   • The complete solution set is {-1, 3}, so the correct response is:
     • {−1, 3}

3. For the number line with an open point at -3 and solid line extending left, and an open point at 3 with a solid line extending right:

   • The solution set represented is x < −3 or x > 3. Therefore, the correct response is:
     • x < −3 or x > 3

4. For the number line with open points at -8 and -2, and a solid line extending between them:

   • The correct solution set represented is x > −8 and x < −2. Therefore, the correct response is:
     • x > −8 and x < −2

5. For the number line with closed points at 9 and 10, with a solid line extending from 10 to the right and from 9 to the left:

   • The correct solution set represented is m ≥ 10 or m ≤ 9. Therefore, the correct response is:
     • m ≥ 10 or m ≤ 9

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