Math / Algebra

QuestionXPRESSIONS \& EQUATIONS - $5 / 10$
Which of the options show a solution set that is true for the inequality below? Select all that apply. $9(2+x)<54$ A) $0,1,2,3$ B) $-1,-2,43,-4$ C) $5,6,7,8$ D) $8,10,12,14$ You can earn 5 coins

Studdy Solution

STEP 1

What is this asking? We need to find which sets of numbers make the inequality $9(2+x) < 54$ true. Watch out! Don't forget to try all the numbers in each set; even if one works, the others might not!
Also, remember the inequality is less than, not less than or equal to.

STEP 2

1. Simplify the inequality
2. Test the solution sets

STEP 3

Alright, let's kick things off by distributing that $9$ across the parentheses!
We're doing this to get the $x$ term a little more isolated.
So, $9$ times $2$ gives us $18$ , and $9$ times $x$ gives us $9x$ .
Our inequality now looks like this: $18 + 9x < 54$

STEP 4

Now, let's isolate that $x$ term even more!
We've got an $18$ hanging around with it, so let's subtract $18$ from both sides of the inequality to keep things balanced.
Remember, what we do to one side, we must do to the other! $18 + 9x - 18 < 54 - 18$ $9x < 36$

STEP 5

Almost there!
We want to get $x$ all by itself, so we'll divide both sides by $9$ .
Since $9$ divided by $9$ is $1$ , we're left with just $x$ on one side.
And $36$ divided by $9$ is $4$ .
So, our simplified inequality is: $x < 4$

STEP 6

Set A has $0, 1, 2,$ and $3$ .
Are all these numbers less than $4$ ?
Yes! So, set A works!

STEP 7

Set B has $-1, -2, 43,$ and $-4$ .
While $-1$ , $-2$ , and $-4$ are less than $4$ , $43$ is not less than $4$ .
So, set B doesn't work because all the numbers in the set must satisfy the inequality.

STEP 8

Set C has $5, 6, 7,$ and $8$ .
None of these numbers are less than $4$ .
So, set C doesn't work.

STEP 9

Set D has $8, 10, 12,$ and $14$ .
None of these numbers are less than $4$ .
So, set D doesn't work.

STEP 10

The solution set that makes the inequality true is A.

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QuestionXPRESSIONS \& EQUATIONS - $5 / 10$
Which of the options show a solution set that is true for the inequality below? Select all that apply. $9(2+x)<54$ A) $0,1,2,3$ B) $-1,-2,43,-4$ C) $5,6,7,8$ D) $8,10,12,14$ You can earn 5 coins

Studdy Solution

STEP 1

What is this asking? We need to find which sets of numbers make the inequality $9(2+x) < 54$ true. Watch out! Don't forget to try all the numbers in each set; even if one works, the others might not!
Also, remember the inequality is less than, not less than or equal to.

STEP 2

1. Simplify the inequality
2. Test the solution sets

STEP 3

Alright, let's kick things off by distributing that $9$ across the parentheses!
We're doing this to get the $x$ term a little more isolated.
So, $9$ times $2$ gives us $18$ , and $9$ times $x$ gives us $9x$ .
Our inequality now looks like this: $18 + 9x < 54$

STEP 4

Now, let's isolate that $x$ term even more!
We've got an $18$ hanging around with it, so let's subtract $18$ from both sides of the inequality to keep things balanced.
Remember, what we do to one side, we must do to the other! $18 + 9x - 18 < 54 - 18$ $9x < 36$

STEP 5

Almost there!
We want to get $x$ all by itself, so we'll divide both sides by $9$ .
Since $9$ divided by $9$ is $1$ , we're left with just $x$ on one side.
And $36$ divided by $9$ is $4$ .
So, our simplified inequality is: $x < 4$

STEP 6

Set A has $0, 1, 2,$ and $3$ .
Are all these numbers less than $4$ ?
Yes! So, set A works!

STEP 7

Set B has $-1, -2, 43,$ and $-4$ .
While $-1$ , $-2$ , and $-4$ are less than $4$ , $43$ is not less than $4$ .
So, set B doesn't work because all the numbers in the set must satisfy the inequality.

STEP 8

Set C has $5, 6, 7,$ and $8$ .
None of these numbers are less than $4$ .
So, set C doesn't work.

STEP 9

Set D has $8, 10, 12,$ and $14$ .
None of these numbers are less than $4$ .
So, set D doesn't work.

STEP 10

The solution set that makes the inequality true is A.

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Studdy Solution

STEP 1

What is this asking? We need to find which sets of numbers make the inequality 9(2+x)<549(2+x) < 549(2+x)<54 true. Watch out! Don't forget to try *all* the numbers in each set; even if one works, the others might not!Also, remember the inequality is *less than*, not less than or equal to.

STEP 2

1. Simplify the inequality2. Test the solution sets

STEP 3

Alright, let's **kick things off** by distributing that 999 across the parentheses!We're doing this to get the xxx term a little more isolated.So, 999 times 222 gives us 181818, and 999 times xxx gives us 9x9x9x.Our inequality now looks like this: 18+9x<5418 + 9x < 5418+9x<54

STEP 4

STEP 5

Almost there!We want to get xxx all by itself, so we'll **divide both sides** by 999.Since 999 divided by 999 is 111, we're left with just xxx on one side.And 363636 divided by 999 is 444.So, our simplified inequality is: x<4x < 4x<4

STEP 6

Set A has 0,1,2,0, 1, 2,0,1,2, and 333.Are all these numbers less than 444?Yes! So, set A **works**!

STEP 7

Set B has −1,−2,43,-1, -2, 43,−1,−2,43, and −4-4−4.While −1-1−1, −2-2−2, and −4-4−4 are less than 444, 434343 is *not* less than 444.So, set B **doesn't work** because *all* the numbers in the set must satisfy the inequality.

STEP 8

Set C has 5,6,7,5, 6, 7,5,6,7, and 888.None of these numbers are less than 444.So, set C **doesn't work**.

STEP 9

Set D has 8,10,12,8, 10, 12,8,10,12, and 141414.None of these numbers are less than 444.So, set D **doesn't work**.

STEP 10

The solution set that makes the inequality true is A.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find which sets of numbers make the inequality $9(2+x) < 54$ true. Watch out! Don't forget to try all the numbers in each set; even if one works, the others might not!
Also, remember the inequality is less than, not less than or equal to.

1. Simplify the inequality
2. Test the solution sets

Alright, let's kick things off by distributing that $9$ across the parentheses!
We're doing this to get the $x$ term a little more isolated.
So, $9$ times $2$ gives us $18$ , and $9$ times $x$ gives us $9x$ .
Our inequality now looks like this: $18 + 9x < 54$

Almost there!
We want to get $x$ all by itself, so we'll divide both sides by $9$ .
Since $9$ divided by $9$ is $1$ , we're left with just $x$ on one side.
And $36$ divided by $9$ is $4$ .
So, our simplified inequality is: $x < 4$

Set A has $0, 1, 2,$ and $3$ .
Are all these numbers less than $4$ ?
Yes! So, set A works!

Set B has $-1, -2, 43,$ and $-4$ .
While $-1$ , $-2$ , and $-4$ are less than $4$ , $43$ is not less than $4$ .
So, set B doesn't work because all the numbers in the set must satisfy the inequality.

Set C has $5, 6, 7,$ and $8$ .
None of these numbers are less than $4$ .
So, set C doesn't work.

Set D has $8, 10, 12,$ and $14$ .
None of these numbers are less than $4$ .
So, set D doesn't work.