Which of the following gives a set of numbers that are all solutions of the inequality x + 6 < 9 ?

a. { -10, -7, -2, -1 }
b. { -6, -3, 0, 3 }
c. { -5, -1, 3, 6 }
d. { 4,7, 10, 16 }

x + 6 < 9 Subtract 6 to both sides

x + 6 - 6 < 9 - 6

x < 3

All numbers less of 3

Answer a

To find the set of numbers that are all solutions of the inequality x + 6 < 9, we need to solve the inequality.

Let's solve it step-by-step:

1. Start with the inequality: x + 6 < 9.

2. Subtract 6 from both sides of the inequality to isolate x: x + 6 - 6 < 9 - 6.

This simplifies to: x < 3.

The inequality x < 3 means that any number less than 3 would satisfy the inequality.

Now, let's go through the options and check which set of numbers satisfies the inequality:

a. {-10, -7, -2, -1}: None of these numbers are less than 3.

b. {-6, -3, 0, 3}: Only -6 and -3 are less than 3, so this set satisfies the inequality.

c. {-5, -1, 3, 6}: Only -5 and -1 are less than 3, so this set satisfies the inequality.

d. {4, 7, 10, 16}: None of these numbers are less than 3.

Therefore, the sets of numbers that are all solutions of the inequality x + 6 < 9 are the sets b. {-6, -3, 0, 3} and c. {-5, -1, 3, 6}.

To find the set of numbers that are all solutions of the inequality x + 6 < 9, we need to solve the inequality by isolating the variable, x.

First, let's subtract 6 from both sides of the inequality:
x + 6 - 6 < 9 - 6

This simplifies to:
x < 3

Now that we have the simplified inequality x < 3, we can look at the list of sets and determine which set contains numbers that are all less than 3.

a. { -10, -7, -2, -1 }
In this set, all the numbers are less than 3, so it could be a possible answer.

b. { -6, -3, 0, 3 }
In this set, the numbers -6 and -3 are less than 3. However, 0 and 3 are not less than 3, so this set does not contain all numbers that are solutions of the inequality.

c. { -5, -1, 3, 6 }
In this set, three of the numbers (-5, -1, and 3) are less than 3. However, 6 is greater than 3, so this set does not contain all numbers that are solutions of the inequality.

d. { 4, 7, 10, 16 }
In this set, all the numbers are greater than 3, so it does not contain any numbers that are solutions of the inequality.

Based on the analysis above, the set that gives a list of numbers that are all solutions of the inequality x + 6 < 9 is option a. { -10, -7, -2, -1 }.