Solved on Feb 04, 2024

Solve for $w$ in the equation $5=-\frac{1}{w-6}$ . Simplify the solution $w=$ .

STEP 1

Assumptions
1. We are given the equation $5 = -\frac{1}{w-6}$ .
2. We need to solve for the variable $w$ .

STEP 2

To solve for $w$ , we first want to isolate the fraction on one side of the equation. We can start by taking the reciprocal of both sides of the equation to get rid of the fraction.
$\frac{1}{5} = - (w - 6)$

STEP 3

Now, we can distribute the negative sign on the right side of the equation.
$\frac{1}{5} = -w + 6$

STEP 4

Next, we want to isolate $w$ on one side of the equation. We can do this by adding $w$ to both sides of the equation.
$\frac{1}{5} + w = 6$

STEP 5

Now, we subtract $\frac{1}{5}$ from both sides of the equation to solve for $w$ .
$w = 6 - \frac{1}{5}$

STEP 6

To subtract the fraction from the whole number, we can write $6$ as a fraction with the same denominator as $\frac{1}{5}$ .
$w = \frac{6 \times 5}{5} - \frac{1}{5}$

STEP 7

Now, perform the multiplication in the numerator of the first fraction.
$w = \frac{30}{5} - \frac{1}{5}$

STEP 8

Subtract the fractions by subtracting their numerators.
$w = \frac{30 - 1}{5}$

STEP 9

Perform the subtraction in the numerator.
$w = \frac{29}{5}$

STEP 10

Finally, we can convert the improper fraction to a mixed number if desired.
$w = 5 \frac{4}{5}$
The solution for $w$ is $w = \frac{29}{5}$ or $w = 5 \frac{4}{5}$ .

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Solve for $w$ in the equation $5=-\frac{1}{w-6}$ . Simplify the solution $w=$ .

STEP 1

Assumptions
1. We are given the equation $5 = -\frac{1}{w-6}$ .
2. We need to solve for the variable $w$ .

STEP 2

To solve for $w$ , we first want to isolate the fraction on one side of the equation. We can start by taking the reciprocal of both sides of the equation to get rid of the fraction.
$\frac{1}{5} = - (w - 6)$

STEP 3

Now, we can distribute the negative sign on the right side of the equation.
$\frac{1}{5} = -w + 6$

STEP 4

Next, we want to isolate $w$ on one side of the equation. We can do this by adding $w$ to both sides of the equation.
$\frac{1}{5} + w = 6$

STEP 5

Now, we subtract $\frac{1}{5}$ from both sides of the equation to solve for $w$ .
$w = 6 - \frac{1}{5}$

STEP 6

To subtract the fraction from the whole number, we can write $6$ as a fraction with the same denominator as $\frac{1}{5}$ .
$w = \frac{6 \times 5}{5} - \frac{1}{5}$

STEP 7

Now, perform the multiplication in the numerator of the first fraction.
$w = \frac{30}{5} - \frac{1}{5}$

STEP 8

Subtract the fractions by subtracting their numerators.
$w = \frac{30 - 1}{5}$

STEP 9

Perform the subtraction in the numerator.
$w = \frac{29}{5}$

STEP 10

Finally, we can convert the improper fraction to a mixed number if desired.
$w = 5 \frac{4}{5}$
The solution for $w$ is $w = \frac{29}{5}$ or $w = 5 \frac{4}{5}$ .

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Solve for www in the equation 5=−1w−65=-\frac{1}{w-6}5=−w−61​. Simplify the solution w=w=w=.

STEP 1

Assumptions1. We are given the equation 5=−1w−65 = -\frac{1}{w-6}5=−w−61​.2. We need to solve for the variable www.

STEP 2

To solve for www, we first want to isolate the fraction on one side of the equation. We can start by taking the reciprocal of both sides of the equation to get rid of the fraction.15=−(w−6)\frac{1}{5} = - (w - 6)51​=−(w−6)

STEP 3

Now, we can distribute the negative sign on the right side of the equation.15=−w+6\frac{1}{5} = -w + 651​=−w+6

STEP 4

Next, we want to isolate www on one side of the equation. We can do this by adding www to both sides of the equation.15+w=6\frac{1}{5} + w = 651​+w=6

STEP 5

Now, we subtract 15\frac{1}{5}51​ from both sides of the equation to solve for www.w=6−15w = 6 - \frac{1}{5}w=6−51​

STEP 6

To subtract the fraction from the whole number, we can write 666 as a fraction with the same denominator as 15\frac{1}{5}51​.w=6×55−15w = \frac{6 \times 5}{5} - \frac{1}{5}w=56×5​−51​

STEP 7

Now, perform the multiplication in the numerator of the first fraction.w=305−15w = \frac{30}{5} - \frac{1}{5}w=530​−51​

STEP 8

Subtract the fractions by subtracting their numerators.w=30−15w = \frac{30 - 1}{5}w=530−1​

STEP 9

Perform the subtraction in the numerator.w=295w = \frac{29}{5}w=529​

STEP 10

Finally, we can convert the improper fraction to a mixed number if desired.w=545w = 5 \frac{4}{5}w=554​The solution for www is w=295w = \frac{29}{5}w=529​ or w=545w = 5 \frac{4}{5}w=554​.

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

Solve for $w$ in the equation $5=-\frac{1}{w-6}$ . Simplify the solution $w=$ .

Assumptions
1. We are given the equation $5 = -\frac{1}{w-6}$ .
2. We need to solve for the variable $w$ .

To solve for $w$ , we first want to isolate the fraction on one side of the equation. We can start by taking the reciprocal of both sides of the equation to get rid of the fraction.
$\frac{1}{5} = - (w - 6)$

Now, we can distribute the negative sign on the right side of the equation.
$\frac{1}{5} = -w + 6$

Next, we want to isolate $w$ on one side of the equation. We can do this by adding $w$ to both sides of the equation.
$\frac{1}{5} + w = 6$

Now, we subtract $\frac{1}{5}$ from both sides of the equation to solve for $w$ .
$w = 6 - \frac{1}{5}$

To subtract the fraction from the whole number, we can write $6$ as a fraction with the same denominator as $\frac{1}{5}$ .
$w = \frac{6 \times 5}{5} - \frac{1}{5}$

Now, perform the multiplication in the numerator of the first fraction.
$w = \frac{30}{5} - \frac{1}{5}$

Subtract the fractions by subtracting their numerators.
$w = \frac{30 - 1}{5}$

Perform the subtraction in the numerator.
$w = \frac{29}{5}$

Finally, we can convert the improper fraction to a mixed number if desired.
$w = 5 \frac{4}{5}$
The solution for $w$ is $w = \frac{29}{5}$ or $w = 5 \frac{4}{5}$ .