Solved on Nov 05, 2023

Solve the inequality: $\frac{b}{25} + 7 > 5$ . Find the range of $b$ values.

STEP 1

Assumptions1. We are given that seven more than the quotient of a number $b$ and25 is greater than5. . We need to write and solve the inequality, and then graph the solution.

STEP 2

First, let's write the inequality based on the given statement."Seven more than the quotient of a number $b$ and25 is greater than5" can be written as $\frac{b}{25} +7 >5$

STEP 3

Now, let's solve the inequality. First, we can isolate the fraction by subtracting7 from both sides of the inequality.
$\frac{b}{25} +7 -7 >5 -7$

STEP 4

implify the inequality.
$\frac{b}{25} > -2$

STEP 5

Next, to solve for $b$ , we can multiply both sides of the inequality by25.
$25 \cdot \frac{b}{25} >25 \cdot -2$

STEP 6

implify the inequality to find the value of $b$ .
$b > -50$ So, the number $b$ is greater than -50.

STEP 7

Now, let's fill in the boxes in the given array.
For the first row, $\frac{\square}{25}+7 \square5$ , we can fill in $b$ for the first box and $>$ for the second box, based on our inequality $\frac{b}{25} +7 >5$ .
For the second row, $\frac{\square}{25} \square-2$ , we can fill in $b$ for the first box and $>$ for the second box, based on our inequality $\frac{b}{25} > -2$ .
For the third row, $b \square \square$ , we can fill in $>$ for the first box and $-50$ for the second box, based on our inequality $b > -50$ .
So, the filled array is $\begin{array}{c} \frac{b}{25}+7 >5 \\ \frac{b}{25} > -2 \\ b > -50\end{array}$

STEP 8

Finally, let's graph the solution. The solution is all numbers greater than -50. On a number line, this can be represented by an open circle at -50 (since -50 is not included in the solution) and an arrow pointing to the right (indicating all numbers greater than -50).

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Solve the inequality: $\frac{b}{25} + 7 > 5$ . Find the range of $b$ values.

STEP 1

Assumptions1. We are given that seven more than the quotient of a number $b$ and25 is greater than5. . We need to write and solve the inequality, and then graph the solution.

STEP 2

First, let's write the inequality based on the given statement."Seven more than the quotient of a number $b$ and25 is greater than5" can be written as $\frac{b}{25} +7 >5$

STEP 3

Now, let's solve the inequality. First, we can isolate the fraction by subtracting7 from both sides of the inequality.
$\frac{b}{25} +7 -7 >5 -7$

STEP 4

implify the inequality.
$\frac{b}{25} > -2$

STEP 5

Next, to solve for $b$ , we can multiply both sides of the inequality by25.
$25 \cdot \frac{b}{25} >25 \cdot -2$

STEP 6

implify the inequality to find the value of $b$ .
$b > -50$ So, the number $b$ is greater than -50.

STEP 7

STEP 8

Finally, let's graph the solution. The solution is all numbers greater than -50. On a number line, this can be represented by an open circle at -50 (since -50 is not included in the solution) and an arrow pointing to the right (indicating all numbers greater than -50).

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Solve the inequality: b25+7>5\frac{b}{25} + 7 > 525b​+7>5. Find the range of bbb values.

STEP 1

Assumptions1. We are given that seven more than the quotient of a number bbb and25 is greater than5. . We need to write and solve the inequality, and then graph the solution.

STEP 2

First, let's write the inequality based on the given statement."Seven more than the quotient of a number bbb and25 is greater than5" can be written asb25+7>5\frac{b}{25} +7 >525b​+7>5

STEP 3

Now, let's solve the inequality. First, we can isolate the fraction by subtracting7 from both sides of the inequality.b25+7−7>5−7\frac{b}{25} +7 -7 >5 -725b​+7−7>5−7

STEP 4

implify the inequality.b25>−2\frac{b}{25} > -225b​>−2

STEP 5

Next, to solve for bbb, we can multiply both sides of the inequality by25.25⋅b25>25⋅−225 \cdot \frac{b}{25} >25 \cdot -225⋅25b​>25⋅−2

STEP 6

implify the inequality to find the value of bbb.b>−50b > -50b>−50So, the number bbb is greater than -50.

STEP 7

STEP 8

Finally, let's graph the solution. The solution is all numbers greater than -50. On a number line, this can be represented by an open circle at -50 (since -50 is not included in the solution) and an arrow pointing to the right (indicating all numbers greater than -50).

Start learning now

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

Solve the inequality: $\frac{b}{25} + 7 > 5$ . Find the range of $b$ values.

Assumptions1. We are given that seven more than the quotient of a number $b$ and25 is greater than5. . We need to write and solve the inequality, and then graph the solution.

First, let's write the inequality based on the given statement."Seven more than the quotient of a number $b$ and25 is greater than5" can be written as $\frac{b}{25} +7 >5$

Now, let's solve the inequality. First, we can isolate the fraction by subtracting7 from both sides of the inequality.
$\frac{b}{25} +7 -7 >5 -7$

implify the inequality.
$\frac{b}{25} > -2$

Next, to solve for $b$ , we can multiply both sides of the inequality by25.
$25 \cdot \frac{b}{25} >25 \cdot -2$

implify the inequality to find the value of $b$ .
$b > -50$ So, the number $b$ is greater than -50.