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

STEP 2

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

STEP 3

To solve for y, we need to get rid of the fraction by multiplying all parts of the inequality by.
$2 \\times < \left(\frac{y+3}{}\right) \\times <3.125 \\times$

STEP 4

Perform the multiplication.
$8 < y+3 <12.$

STEP 5

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

STEP 6

Perform the subtraction.
$5 < y <9.5$

STEP 7

The solution to the inequality is $5 < y <9.5$ . In interval notation, this is expressed as $(5,9.5)$ , where the parentheses indicate that the endpoints are not included in the solution.
So, the solution to the inequality 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 inequality is given as $\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}$ . . We need to solve for y.
3. The solution should be expressed in interval notation.

STEP 2

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

STEP 3

To solve for y, we need to get rid of the fraction by multiplying all parts of the inequality by.
$2 \\times < \left(\frac{y+3}{}\right) \\times <3.125 \\times$

STEP 4

Perform the multiplication.
$8 < y+3 <12.$

STEP 5

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

STEP 6

Perform the subtraction.
$5 < y <9.5$

STEP 7

The solution to the inequality is $5 < y <9.5$ . In interval notation, this is expressed as $(5,9.5)$ , where the parentheses indicate that the endpoints are not included in the solution.
So, the solution to the inequality 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 inequality is given as 168<y+34<258\frac{16}{8}<\frac{y+3}{4}<\frac{25}{8}816​<4y+3​<825​. . We need to solve for y.3. The solution should be expressed in interval notation.

STEP 2

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

STEP 3

To solve for y, we need to get rid of the fraction by multiplying all parts of the inequality by.2times<(y+3)times<3.125times2 \\times < \left(\frac{y+3}{}\right) \\times <3.125 \\times2times<(y+3​)times<3.125times

STEP 4

Perform the multiplication.8<y+3<12.8 < y+3 <12.8<y+3<12.

STEP 5

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

STEP 6

Perform the subtraction.5<y<9.55 < y <9.55<y<9.5

STEP 7

The solution to the inequality is 5<y<9.55 < y <9.55<y<9.5. In interval notation, this is expressed as (5,9.5)(5,9.5)(5,9.5), where the parentheses indicate that the endpoints are not included in the solution.So, the solution to the inequality is (5,9.5)(5,9.5)(5,9.5).

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Studdy solves anything!

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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.

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

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

To solve for y, we need to get rid of the fraction by multiplying all parts of the inequality by.
$2 \\times < \left(\frac{y+3}{}\right) \\times <3.125 \\times$

Perform the multiplication.
$8 < y+3 <12.$

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

Perform the subtraction.
$5 < y <9.5$

The solution to the inequality is $5 < y <9.5$ . In interval notation, this is expressed as $(5,9.5)$ , where the parentheses indicate that the endpoints are not included in the solution.
So, the solution to the inequality is $(5,9.5)$ .