QuestionGraph the solution to the compound inequality $4 \geq y + 14 > -3$ . Plot endpoints, change one to open, and delete a segment.

Studdy Solution

STEP 1

Assumptions1. The inequality is $4 \geq y+14>-3$ . We need to solve for $y$
3. The inequality is a compound inequality, which means it combines two inequalities

STEP 2

First, we need to separate the compound inequality into two separate inequalities. $4 \geq y+14$ $y+14 > -$

STEP 3

Now, we will solve each inequality separately. Starting with the first inequality, we subtract14 from both sides to isolate $y$ .
$-14 \geq y$

STEP 4

Calculate the result.
$-10 \geq y$

STEP 5

Now, we will solve the second inequality. Subtract14 from both sides to isolate $y$ .
$y+14 -14 > -3 -14$

STEP 6

Calculate the result.
$y > -17$

STEP 7

Now we have two inequalities that describe the range of $y$ .
$-10 \geq y > -17$

STEP 8

To graph this solution, we plot the points $-10$ and $-17$ on a number line. The value $y=-10$ is included in the solution (as indicated by the $\geq$ symbol), so we use a closed dot. The value $y=-17$ is not included in the solution (as indicated by the $>$ symbol), so we use an open dot.

STEP 9

Draw a line segment between the two points to indicate all the numbers in between are part of the solution.
The solution to the inequality is $-17 < y \leq -$ and the graph represents all numbers between $-17$ (not included) and $-$ (included).

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QuestionGraph the solution to the compound inequality $4 \geq y + 14 > -3$ . Plot endpoints, change one to open, and delete a segment.

Studdy Solution

STEP 1

Assumptions1. The inequality is $4 \geq y+14>-3$ . We need to solve for $y$
3. The inequality is a compound inequality, which means it combines two inequalities

STEP 2

First, we need to separate the compound inequality into two separate inequalities. $4 \geq y+14$ $y+14 > -$

STEP 3

Now, we will solve each inequality separately. Starting with the first inequality, we subtract14 from both sides to isolate $y$ .
$-14 \geq y$

STEP 4

Calculate the result.
$-10 \geq y$

STEP 5

Now, we will solve the second inequality. Subtract14 from both sides to isolate $y$ .
$y+14 -14 > -3 -14$

STEP 6

Calculate the result.
$y > -17$

STEP 7

Now we have two inequalities that describe the range of $y$ .
$-10 \geq y > -17$

STEP 8

To graph this solution, we plot the points $-10$ and $-17$ on a number line. The value $y=-10$ is included in the solution (as indicated by the $\geq$ symbol), so we use a closed dot. The value $y=-17$ is not included in the solution (as indicated by the $>$ symbol), so we use an open dot.

STEP 9

Draw a line segment between the two points to indicate all the numbers in between are part of the solution.
The solution to the inequality is $-17 < y \leq -$ and the graph represents all numbers between $-17$ (not included) and $-$ (included).

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QuestionGraph the solution to the compound inequality 4≥y+14>−34 \geq y + 14 > -34≥y+14>−3. Plot endpoints, change one to open, and delete a segment.

Studdy Solution

STEP 1

Assumptions1. The inequality is 4≥y+14>−34 \geq y+14>-34≥y+14>−3 . We need to solve for yyy3. The inequality is a compound inequality, which means it combines two inequalities

STEP 2

First, we need to separate the compound inequality into two separate inequalities.4≥y+144 \geq y+144≥y+14y+14>−y+14 > -y+14>−

STEP 3

Now, we will solve each inequality separately. Starting with the first inequality, we subtract14 from both sides to isolate yyy.−14≥y -14 \geq y−14≥y

STEP 4

Calculate the result.−10≥y-10 \geq y−10≥y

STEP 5

Now, we will solve the second inequality. Subtract14 from both sides to isolate yyy.y+14−14>−3−14y+14 -14 > -3 -14y+14−14>−3−14

STEP 6

Calculate the result.y>−17y > -17y>−17

STEP 7

Now we have two inequalities that describe the range of yyy.−10≥y>−17-10 \geq y > -17−10≥y>−17

STEP 8

STEP 9

Draw a line segment between the two points to indicate all the numbers in between are part of the solution.The solution to the inequality is −17<y≤−-17 < y \leq -−17<y≤− and the graph represents all numbers between −17-17−17 (not included) and −-− (included).

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

QuestionGraph the solution to the compound inequality $4 \geq y + 14 > -3$ . Plot endpoints, change one to open, and delete a segment.

Assumptions1. The inequality is $4 \geq y+14>-3$ . We need to solve for $y$
3. The inequality is a compound inequality, which means it combines two inequalities

First, we need to separate the compound inequality into two separate inequalities. $4 \geq y+14$ $y+14 > -$

Now, we will solve each inequality separately. Starting with the first inequality, we subtract14 from both sides to isolate $y$ .
$-14 \geq y$

Calculate the result.
$-10 \geq y$

Now, we will solve the second inequality. Subtract14 from both sides to isolate $y$ .
$y+14 -14 > -3 -14$

Calculate the result.
$y > -17$

Now we have two inequalities that describe the range of $y$ .
$-10 \geq y > -17$

Draw a line segment between the two points to indicate all the numbers in between are part of the solution.
The solution to the inequality is $-17 < y \leq -$ and the graph represents all numbers between $-17$ (not included) and $-$ (included).