QuestionGraph the solution set for the compound inequality: $\frac{22}{8}<\frac{y+7}{4}<\frac{29}{8}$ .

Studdy Solution

STEP 1

Assumptions1. The inequality is a compound inequality with two parts. . The inequality is in the form of $\frac{a}{b}<\frac{y+c}{d}<\frac{e}{f}$ .
3. We need to graph the solution set of this inequality.

STEP 2

First, we need to solve the compound inequality for $y$ . We can do this by multiplying all parts of the inequality by4 to get rid of the denominator in the middle expression.
$4 \times \frac{22}{8}<4 \times \frac{y+7}{4}<4 \times \frac{29}{8}$

STEP 3

implify the inequality.
$\frac{22}{2}<y+7<\frac{29}{2}$

STEP 4

Further simplify the inequality.
$11<y+7<14.$

STEP 5

Subtract7 from all parts of the inequality to solve for $y$ .
$11-7<y+7-7<14.5-7$

STEP 6

implify the inequality to find the solution set for $y$ .
$4<y<.5$

STEP 7

Now, we need to graph the solution set. Draw a number line and mark the points corresponding to4 and7.5.

STEP 8

Since $y$ is greater than4 and less than7.5, we shade the region between4 and7.5. We use open circles at4 and7.5 to indicate that these values are not included in the solution set.
The solution set is $4<y<7.5$ .

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QuestionGraph the solution set for the compound inequality: $\frac{22}{8}<\frac{y+7}{4}<\frac{29}{8}$ .

Studdy Solution

STEP 1

Assumptions1. The inequality is a compound inequality with two parts. . The inequality is in the form of $\frac{a}{b}<\frac{y+c}{d}<\frac{e}{f}$ .
3. We need to graph the solution set of this inequality.

STEP 2

First, we need to solve the compound inequality for $y$ . We can do this by multiplying all parts of the inequality by4 to get rid of the denominator in the middle expression.
$4 \times \frac{22}{8}<4 \times \frac{y+7}{4}<4 \times \frac{29}{8}$

STEP 3

implify the inequality.
$\frac{22}{2}<y+7<\frac{29}{2}$

STEP 4

Further simplify the inequality.
$11<y+7<14.$

STEP 5

Subtract7 from all parts of the inequality to solve for $y$ .
$11-7<y+7-7<14.5-7$

STEP 6

implify the inequality to find the solution set for $y$ .
$4<y<.5$

STEP 7

Now, we need to graph the solution set. Draw a number line and mark the points corresponding to4 and7.5.

STEP 8

Since $y$ is greater than4 and less than7.5, we shade the region between4 and7.5. We use open circles at4 and7.5 to indicate that these values are not included in the solution set.
The solution set is $4<y<7.5$ .

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QuestionGraph the solution set for the compound inequality: 228<y+74<298 \frac{22}{8}<\frac{y+7}{4}<\frac{29}{8} 822​<4y+7​<829​.

Studdy Solution

STEP 1

Assumptions1. The inequality is a compound inequality with two parts. . The inequality is in the form of ab<y+cd<ef\frac{a}{b}<\frac{y+c}{d}<\frac{e}{f}ba​<dy+c​<fe​.3. We need to graph the solution set of this inequality.

STEP 2

First, we need to solve the compound inequality for yyy. We can do this by multiplying all parts of the inequality by4 to get rid of the denominator in the middle expression.4×228<4×y+74<4×2984 \times \frac{22}{8}<4 \times \frac{y+7}{4}<4 \times \frac{29}{8}4×822​<4×4y+7​<4×829​

STEP 3

implify the inequality.222<y+7<292\frac{22}{2}<y+7<\frac{29}{2}222​<y+7<229​

STEP 4

Further simplify the inequality.11<y+7<14.11<y+7<14.11<y+7<14.

STEP 5

Subtract7 from all parts of the inequality to solve for yyy.11−7<y+7−7<14.5−711-7<y+7-7<14.5-711−7<y+7−7<14.5−7

STEP 6

implify the inequality to find the solution set for yyy.4<y<.54<y<.54<y<.5

STEP 7

Now, we need to graph the solution set. Draw a number line and mark the points corresponding to4 and7.5.

STEP 8

Since yyy is greater than4 and less than7.5, we shade the region between4 and7.5. We use open circles at4 and7.5 to indicate that these values are not included in the solution set.The solution set is 4<y<7.54<y<7.54<y<7.5.

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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.

QuestionGraph the solution set for the compound inequality: $\frac{22}{8}<\frac{y+7}{4}<\frac{29}{8}$ .

Assumptions1. The inequality is a compound inequality with two parts. . The inequality is in the form of $\frac{a}{b}<\frac{y+c}{d}<\frac{e}{f}$ .
3. We need to graph the solution set of this inequality.

First, we need to solve the compound inequality for $y$ . We can do this by multiplying all parts of the inequality by4 to get rid of the denominator in the middle expression.
$4 \times \frac{22}{8}<4 \times \frac{y+7}{4}<4 \times \frac{29}{8}$

implify the inequality.
$\frac{22}{2}<y+7<\frac{29}{2}$

Further simplify the inequality.
$11<y+7<14.$

Subtract7 from all parts of the inequality to solve for $y$ .
$11-7<y+7-7<14.5-7$

implify the inequality to find the solution set for $y$ .
$4<y<.5$

Since $y$ is greater than4 and less than7.5, we shade the region between4 and7.5. We use open circles at4 and7.5 to indicate that these values are not included in the solution set.
The solution set is $4<y<7.5$ .