QuestionSolve the compound inequality $\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}$ and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. The compound inequality is given by $\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}$ . . We need to solve for $y$ .
3. The solution should be expressed in interval notation.

STEP 2

First, we simplify the fractions on the left and right side of the inequality.
$2<\frac{y+}{4}<.125$

STEP 3

Now, we multiply all parts of the inequality by to get rid of the fraction in the middle.
$2 \times < (y+3) <3.125 \times$

STEP 4

Calculate the products on the left and right side of the inequality.
$8 < y+3 <12.$

STEP 5

Next, we subtract3 from all parts of the inequality to isolate $y$ .
$8 -3 < y <12.5 -3$

STEP 6

Calculate the differences on the left and right side of the inequality.
$5 < y <9.5$ This is the solution for $y$ in inequality form.

STEP 7

Finally, we express the solution in interval notation.
The solution in interval notation is $(5,9.5)$ .

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QuestionSolve the compound inequality $\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}$ and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. The compound inequality is given by $\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}$ . . We need to solve for $y$ .
3. The solution should be expressed in interval notation.

STEP 2

First, we simplify the fractions on the left and right side of the inequality.
$2<\frac{y+}{4}<.125$

STEP 3

Now, we multiply all parts of the inequality by to get rid of the fraction in the middle.
$2 \times < (y+3) <3.125 \times$

STEP 4

Calculate the products on the left and right side of the inequality.
$8 < y+3 <12.$

STEP 5

Next, we subtract3 from all parts of the inequality to isolate $y$ .
$8 -3 < y <12.5 -3$

STEP 6

Calculate the differences on the left and right side of the inequality.
$5 < y <9.5$ This is the solution for $y$ in inequality form.

STEP 7

Finally, we express the solution in interval notation.
The solution in interval notation is $(5,9.5)$ .

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QuestionSolve the compound inequality 168<y+34<258\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}816​<4y+3​<825​ and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. The compound inequality is given by 168<y+34<258\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}816​<4y+3​<825​. . We need to solve for yyy.3. The solution should be expressed in interval notation.

STEP 2

First, we simplify the fractions on the left and right side of the inequality.2<y+4<.1252<\frac{y+}{4}<.1252<4y+​<.125

STEP 3

Now, we multiply all parts of the inequality by to get rid of the fraction in the middle.2×<(y+3)<3.125×2 \times < (y+3) <3.125 \times2×<(y+3)<3.125×

STEP 4

Calculate the products on the left and right side of the inequality.8<y+3<12.8 < y+3 <12.8<y+3<12.

STEP 5

Next, we subtract3 from all parts of the inequality to isolate yyy.8−3<y<12.5−38 -3 < y <12.5 -38−3<y<12.5−3

STEP 6

Calculate the differences on the left and right side of the inequality.5<y<9.55 < y <9.55<y<9.5This is the solution for yyy in inequality form.

STEP 7

Finally, we express the solution in interval notation.The solution in interval notation is (5,9.5)(5,9.5)(5,9.5).

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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.

QuestionSolve the compound inequality $\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}$ and express the solution in interval notation.

Assumptions1. The compound inequality is given by $\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}$ . . We need to solve for $y$ .
3. The solution should be expressed in interval notation.

First, we simplify the fractions on the left and right side of the inequality.
$2<\frac{y+}{4}<.125$

Now, we multiply all parts of the inequality by to get rid of the fraction in the middle.
$2 \times < (y+3) <3.125 \times$

Calculate the products on the left and right side of the inequality.
$8 < y+3 <12.$

Next, we subtract3 from all parts of the inequality to isolate $y$ .
$8 -3 < y <12.5 -3$

Calculate the differences on the left and right side of the inequality.
$5 < y <9.5$ This is the solution for $y$ in inequality form.

Finally, we express the solution in interval notation.
The solution in interval notation is $(5,9.5)$ .