Solved on Oct 30, 2023

Solve the inequality $\frac{8}{2} + b > \frac{23}{16}$ . Enter the solution as an interval, using "oo" for $\infty$ , and fractions in reduced form.

STEP 1

Assumptions1. The inequality to solve is $\frac{8}{}+b>\frac{23}{16}$

STEP 2

First, simplify the left side of the inequality. The fraction $\frac{8}{2}$ simplifies to4.
$4+b>\frac{23}{16}$

STEP 3

To isolate $b$ , subtract from both sides of the inequality.
$b>\frac{23}{16}-$

STEP 4

To subtract4 from $\frac{23}{16}$ , we need to express4 as a fraction with16 as the denominator.4 is equivalent to $\frac{64}{16}$ .
$b>\frac{23}{16}-\frac{64}{16}$

STEP 5

Subtract the fractions on the right side of the inequality.
$b>\frac{23-64}{16}$

STEP 6

Calculate the numerator of the fraction on the right side of the inequality.
$b>\frac{-41}{16}$ The solution to the inequality is $b>\frac{-41}{16}$ , or in interval notation, $b\in (\frac{-41}{16}, oo)$ .

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Solve the inequality $\frac{8}{2} + b > \frac{23}{16}$ . Enter the solution as an interval, using "oo" for $\infty$ , and fractions in reduced form.

STEP 1

Assumptions1. The inequality to solve is $\frac{8}{}+b>\frac{23}{16}$

STEP 2

First, simplify the left side of the inequality. The fraction $\frac{8}{2}$ simplifies to4.
$4+b>\frac{23}{16}$

STEP 3

To isolate $b$ , subtract from both sides of the inequality.
$b>\frac{23}{16}-$

STEP 4

To subtract4 from $\frac{23}{16}$ , we need to express4 as a fraction with16 as the denominator.4 is equivalent to $\frac{64}{16}$ .
$b>\frac{23}{16}-\frac{64}{16}$

STEP 5

Subtract the fractions on the right side of the inequality.
$b>\frac{23-64}{16}$

STEP 6

Calculate the numerator of the fraction on the right side of the inequality.
$b>\frac{-41}{16}$ The solution to the inequality is $b>\frac{-41}{16}$ , or in interval notation, $b\in (\frac{-41}{16}, oo)$ .

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Solve the inequality 82+b>2316\frac{8}{2} + b > \frac{23}{16}28​+b>1623​. Enter the solution as an interval, using "oo" for ∞\infty∞, and fractions in reduced form.

STEP 1

Assumptions1. The inequality to solve is 8+b>2316\frac{8}{}+b>\frac{23}{16}8​+b>1623​

STEP 2

First, simplify the left side of the inequality. The fraction 82\frac{8}{2}28​ simplifies to4.4+b>23164+b>\frac{23}{16}4+b>1623​

STEP 3

To isolate bbb, subtract from both sides of the inequality.b>2316−b>\frac{23}{16}-b>1623​−

STEP 4

To subtract4 from 2316\frac{23}{16}1623​, we need to express4 as a fraction with16 as the denominator.4 is equivalent to 6416\frac{64}{16}1664​.b>2316−6416b>\frac{23}{16}-\frac{64}{16}b>1623​−1664​

STEP 5

Subtract the fractions on the right side of the inequality.b>23−6416b>\frac{23-64}{16}b>1623−64​

STEP 6

Calculate the numerator of the fraction on the right side of the inequality.b>−4116b>\frac{-41}{16}b>16−41​The solution to the inequality is b>−4116b>\frac{-41}{16}b>16−41​, or in interval notation, b∈(−4116,oo)b\in (\frac{-41}{16}, oo)b∈(16−41​,oo).

Start learning now

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

Solve the inequality $\frac{8}{2} + b > \frac{23}{16}$ . Enter the solution as an interval, using "oo" for $\infty$ , and fractions in reduced form.

Assumptions1. The inequality to solve is $\frac{8}{}+b>\frac{23}{16}$

First, simplify the left side of the inequality. The fraction $\frac{8}{2}$ simplifies to4.
$4+b>\frac{23}{16}$

To isolate $b$ , subtract from both sides of the inequality.
$b>\frac{23}{16}-$

To subtract4 from $\frac{23}{16}$ , we need to express4 as a fraction with16 as the denominator.4 is equivalent to $\frac{64}{16}$ .
$b>\frac{23}{16}-\frac{64}{16}$

Subtract the fractions on the right side of the inequality.
$b>\frac{23-64}{16}$

Calculate the numerator of the fraction on the right side of the inequality.
$b>\frac{-41}{16}$ The solution to the inequality is $b>\frac{-41}{16}$ , or in interval notation, $b\in (\frac{-41}{16}, oo)$ .