Question Solve for $y$ and graph the solution. Solve the system of linear inequalities: $-13y+6<-15y-6$ or $2y+3\geq8-3y$ . Plot the endpoints and modify the graph.

Studdy Solution

STEP 1

Assumptions1. We are given two inequalities $-13y +6 < -15y -6$ and $y +3 \geq8 -3y$ . . We need to solve for $y$ in each inequality and graph the solution.
3. We will plot the endpoints and select an endpoint to change it from closed to open.
4. We will select the middle of a segment, ray, or line to delete it.

STEP 2

Let's start by solving the first inequality. We can do this by first adding $15y$ to both sides to get rid of the $-15y$ on the right side.
$-13y +15y +6 < -6$

STEP 3

implify the left side of the inequality.
$2y +6 < -6$

STEP 4

Subtract $6$ from both sides to isolate $2y$ on the left side.
$2y < -12$

STEP 5

Divide both sides by $2$ to solve for $y$ .
$y < -$

STEP 6

Now, let's solve the second inequality. We can do this by first adding $3y$ to both sides to get rid of the $-3y$ on the right side.
$2y +3y +3 \geq8$

STEP 7

implify the left side of the inequality.
$5y +3 \geq$

STEP 8

Subtract $3$ from both sides to isolate $5y$ on the left side.
$5y \geq5$

STEP 9

Divide both sides by $5$ to solve for $y$ .
$y \geq$

STEP 10

Now, let's graph the solutions. The first inequality, $y < -6$ , is an open interval because it does not include $-6$ . So, we draw an open circle at $-6$ and an arrow pointing to the left, indicating all numbers less than $-6$ .
The second inequality, $y \geq$ , is a closed interval because it includes $. So, we draw a closed circle at$ and an arrow pointing to the right, indicating all numbers greater than or equal to $$.
The solution to the given inequalities is the union of these two intervals.

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Question Solve for $y$ and graph the solution. Solve the system of linear inequalities: $-13y+6<-15y-6$ or $2y+3\geq8-3y$ . Plot the endpoints and modify the graph.

Studdy Solution

STEP 1

STEP 2

Let's start by solving the first inequality. We can do this by first adding $15y$ to both sides to get rid of the $-15y$ on the right side.
$-13y +15y +6 < -6$

STEP 3

implify the left side of the inequality.
$2y +6 < -6$

STEP 4

Subtract $6$ from both sides to isolate $2y$ on the left side.
$2y < -12$

STEP 5

Divide both sides by $2$ to solve for $y$ .
$y < -$

STEP 6

Now, let's solve the second inequality. We can do this by first adding $3y$ to both sides to get rid of the $-3y$ on the right side.
$2y +3y +3 \geq8$

STEP 7

implify the left side of the inequality.
$5y +3 \geq$

STEP 8

Subtract $3$ from both sides to isolate $5y$ on the left side.
$5y \geq5$

STEP 9

Divide both sides by $5$ to solve for $y$ .
$y \geq$

STEP 10

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Question Solve for yyy and graph the solution. Solve the system of linear inequalities: −13y+6<−15y−6-13y+6<-15y-6−13y+6<−15y−6 or 2y+3≥8−3y2y+3\geq8-3y2y+3≥8−3y. Plot the endpoints and modify the graph.

Studdy Solution

STEP 1

STEP 2

Let's start by solving the first inequality. We can do this by first adding 15y15y15y to both sides to get rid of the −15y-15y−15y on the right side.−13y+15y+6<−6-13y +15y +6 < -6−13y+15y+6<−6

STEP 3

implify the left side of the inequality.2y+6<−62y +6 < -62y+6<−6

STEP 4

Subtract 666 from both sides to isolate 2y2y2y on the left side.2y<−122y < -122y<−12

STEP 5

Divide both sides by 222 to solve for yyy.y<−y < -y<−

STEP 6

Now, let's solve the second inequality. We can do this by first adding 3y3y3y to both sides to get rid of the −3y-3y−3y on the right side.2y+3y+3≥82y +3y +3 \geq82y+3y+3≥8

STEP 7

implify the left side of the inequality.5y+3≥5y +3 \geq5y+3≥

STEP 8

Subtract 333 from both sides to isolate 5y5y5y on the left side.5y≥55y \geq55y≥5

STEP 9

Divide both sides by 555 to solve for yyy.y≥y \geqy≥

STEP 10

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Studdy solves anything!

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

Question Solve for $y$ and graph the solution. Solve the system of linear inequalities: $-13y+6<-15y-6$ or $2y+3\geq8-3y$ . Plot the endpoints and modify the graph.

Let's start by solving the first inequality. We can do this by first adding $15y$ to both sides to get rid of the $-15y$ on the right side.
$-13y +15y +6 < -6$

implify the left side of the inequality.
$2y +6 < -6$

Subtract $6$ from both sides to isolate $2y$ on the left side.
$2y < -12$

Divide both sides by $2$ to solve for $y$ .
$y < -$

Now, let's solve the second inequality. We can do this by first adding $3y$ to both sides to get rid of the $-3y$ on the right side.
$2y +3y +3 \geq8$

implify the left side of the inequality.
$5y +3 \geq$

Subtract $3$ from both sides to isolate $5y$ on the left side.
$5y \geq5$

Divide both sides by $5$ to solve for $y$ .
$y \geq$