Solved on Jan 18, 2024

Find values of x that satisfy the inequality $17 > -2x + 11$ . Circle all applicable options: $\frac{1}{11}$ , $-2 \frac{9}{17}$ , $-3 \frac{4}{9}$ .

STEP 1

Assumptions
1. We are given the inequality $17 > -2x + 11$ .
2. We need to determine which of the given numbers satisfy the inequality.
3. The given numbers are: $256,123$ , $\frac{1}{11}$ , $-2 \frac{9}{17}$ , $-3$ , $-3 \frac{4}{9}$ , and $-15,678$ .

STEP 2

First, we need to isolate the variable $x$ on one side of the inequality. To do this, we will subtract 11 from both sides of the inequality.
$17 - 11 > -2x + 11 - 11$

STEP 3

Simplify the inequality by performing the subtraction.
$6 > -2x$

STEP 4

Now, we need to solve for $x$ . Since $-2x$ is multiplied by $-2$ , we will divide both sides of the inequality by $-2$ to isolate $x$ . Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
$\frac{6}{-2} < x$

STEP 5

Perform the division to find the value of $x$ .
$-3 < x$

STEP 6

The inequality $-3 < x$ means that $x$ must be greater than $-3$ . We will now check which of the given numbers are greater than $-3$ .

STEP 7

Check option (a) $256,123$ :
Since $256,123$ is much greater than $-3$ , this number satisfies the inequality.

STEP 8

Check option (b) $\frac{1}{11}$ :
Since $\frac{1}{11}$ is greater than $-3$ , this number satisfies the inequality.

STEP 9

Check option (c) $-2 \frac{9}{17}$ :
Since $-2 \frac{9}{17}$ is greater than $-3$ , this number satisfies the inequality.

STEP 10

Check option (d) $-3$ :
Since $-3$ is not greater than $-3$ , it does not satisfy the inequality.

STEP 11

Check option (e) $-3 \frac{4}{9}$ :
Since $-3 \frac{4}{9}$ is less than $-3$ , it does not satisfy the inequality.

STEP 12

Check option (f) $-15,678$ :
Since $-15,678$ is less than $-3$ , it does not satisfy the inequality.

STEP 13

The numbers that satisfy the inequality $17 > -2x + 11$ are:
(a) $256,123$ , (b) $\frac{1}{11}$ , and (c) $-2 \frac{9}{17}$ .

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Find values of x that satisfy the inequality $17 > -2x + 11$ . Circle all applicable options: $\frac{1}{11}$ , $-2 \frac{9}{17}$ , $-3 \frac{4}{9}$ .

STEP 1

Assumptions
1. We are given the inequality $17 > -2x + 11$ .
2. We need to determine which of the given numbers satisfy the inequality.
3. The given numbers are: $256,123$ , $\frac{1}{11}$ , $-2 \frac{9}{17}$ , $-3$ , $-3 \frac{4}{9}$ , and $-15,678$ .

STEP 2

First, we need to isolate the variable $x$ on one side of the inequality. To do this, we will subtract 11 from both sides of the inequality.
$17 - 11 > -2x + 11 - 11$

STEP 3

Simplify the inequality by performing the subtraction.
$6 > -2x$

STEP 4

Now, we need to solve for $x$ . Since $-2x$ is multiplied by $-2$ , we will divide both sides of the inequality by $-2$ to isolate $x$ . Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
$\frac{6}{-2} < x$

STEP 5

Perform the division to find the value of $x$ .
$-3 < x$

STEP 6

The inequality $-3 < x$ means that $x$ must be greater than $-3$ . We will now check which of the given numbers are greater than $-3$ .

STEP 7

Check option (a) $256,123$ :
Since $256,123$ is much greater than $-3$ , this number satisfies the inequality.

STEP 8

Check option (b) $\frac{1}{11}$ :
Since $\frac{1}{11}$ is greater than $-3$ , this number satisfies the inequality.

STEP 9

Check option (c) $-2 \frac{9}{17}$ :
Since $-2 \frac{9}{17}$ is greater than $-3$ , this number satisfies the inequality.

STEP 10

Check option (d) $-3$ :
Since $-3$ is not greater than $-3$ , it does not satisfy the inequality.

STEP 11

Check option (e) $-3 \frac{4}{9}$ :
Since $-3 \frac{4}{9}$ is less than $-3$ , it does not satisfy the inequality.

STEP 12

Check option (f) $-15,678$ :
Since $-15,678$ is less than $-3$ , it does not satisfy the inequality.

STEP 13

The numbers that satisfy the inequality $17 > -2x + 11$ are:
(a) $256,123$ , (b) $\frac{1}{11}$ , and (c) $-2 \frac{9}{17}$ .

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Find values of x that satisfy the inequality 17>−2x+1117 > -2x + 1117>−2x+11. Circle all applicable options: 111\frac{1}{11}111​, −2917-2 \frac{9}{17}−2179​, −349-3 \frac{4}{9}−394​.

STEP 1

STEP 2

First, we need to isolate the variable xxx on one side of the inequality. To do this, we will subtract 11 from both sides of the inequality.17−11>−2x+11−1117 - 11 > -2x + 11 - 1117−11>−2x+11−11

STEP 3

Simplify the inequality by performing the subtraction.6>−2x6 > -2x6>−2x

STEP 4

STEP 5

Perform the division to find the value of xxx.−3<x-3 < x−3<x

STEP 6

The inequality −3<x-3 < x−3<x means that xxx must be greater than −3-3−3. We will now check which of the given numbers are greater than −3-3−3.

STEP 7

Check option (a) 256,123256,123256,123:Since 256,123256,123256,123 is much greater than −3-3−3, this number satisfies the inequality.

STEP 8

Check option (b) 111\frac{1}{11}111​:Since 111\frac{1}{11}111​ is greater than −3-3−3, this number satisfies the inequality.

STEP 9

Check option (c) −2917-2 \frac{9}{17}−2179​:Since −2917-2 \frac{9}{17}−2179​ is greater than −3-3−3, this number satisfies the inequality.

STEP 10

Check option (d) −3-3−3:Since −3-3−3 is not greater than −3-3−3, it does not satisfy the inequality.

STEP 11

Check option (e) −349-3 \frac{4}{9}−394​:Since −349-3 \frac{4}{9}−394​ is less than −3-3−3, it does not satisfy the inequality.

STEP 12

Check option (f) −15,678-15,678−15,678:Since −15,678-15,678−15,678 is less than −3-3−3, it does not satisfy the inequality.

STEP 13

The numbers that satisfy the inequality 17>−2x+1117 > -2x + 1117>−2x+11 are:(a) 256,123256,123256,123, (b) 111\frac{1}{11}111​, and (c) −2917-2 \frac{9}{17}−2179​.

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Find values of x that satisfy the inequality $17 > -2x + 11$ . Circle all applicable options: $\frac{1}{11}$ , $-2 \frac{9}{17}$ , $-3 \frac{4}{9}$ .

First, we need to isolate the variable $x$ on one side of the inequality. To do this, we will subtract 11 from both sides of the inequality.
$17 - 11 > -2x + 11 - 11$

Simplify the inequality by performing the subtraction.
$6 > -2x$

Perform the division to find the value of $x$ .
$-3 < x$

The inequality $-3 < x$ means that $x$ must be greater than $-3$ . We will now check which of the given numbers are greater than $-3$ .

Check option (a) $256,123$ :
Since $256,123$ is much greater than $-3$ , this number satisfies the inequality.

Check option (b) $\frac{1}{11}$ :
Since $\frac{1}{11}$ is greater than $-3$ , this number satisfies the inequality.

Check option (c) $-2 \frac{9}{17}$ :
Since $-2 \frac{9}{17}$ is greater than $-3$ , this number satisfies the inequality.

Check option (d) $-3$ :
Since $-3$ is not greater than $-3$ , it does not satisfy the inequality.

Check option (e) $-3 \frac{4}{9}$ :
Since $-3 \frac{4}{9}$ is less than $-3$ , it does not satisfy the inequality.

Check option (f) $-15,678$ :
Since $-15,678$ is less than $-3$ , it does not satisfy the inequality.

The numbers that satisfy the inequality $17 > -2x + 11$ are:
(a) $256,123$ , (b) $\frac{1}{11}$ , and (c) $-2 \frac{9}{17}$ .