Solved on Jan 18, 2024

Solve for $g$ given the equation $f=\frac{1}{7}(g+h-k)$ .

STEP 1

Assumptions
1. The given equation is $f = \frac{1}{7}(g + h - k)$ .
2. We need to solve for $g$ .
3. The variables $h$ and $k$ are constants or known values.
4. The variable $f$ is a known value or constant.

STEP 2

First, we want to isolate the term containing $g$ on one side of the equation. To do this, we can start by multiplying both sides of the equation by 7 to eliminate the fraction.
$7 \cdot f = 7 \cdot \frac{1}{7}(g + h - k)$

STEP 3

Simplify both sides of the equation by performing the multiplication on the right side and canceling out the 7 in the denominator.
$7f = g + h - k$

STEP 4

Next, we want to isolate $g$ by moving the terms $h$ and $-k$ to the other side of the equation. We can do this by adding $k$ to both sides and subtracting $h$ from both sides.
$7f + h - k = g + h - k + h - k$

STEP 5

Simplify the equation by combining like terms.
$7f + h - k = g$

STEP 6

Now we have isolated $g$ on one side of the equation. The expression $7f + h - k$ is equal to $g$ .
$g = 7f + h - k$
So, the solution for $g$ is:
$g = 7f + h - k$

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Solve for $g$ given the equation $f=\frac{1}{7}(g+h-k)$ .

STEP 1

Assumptions
1. The given equation is $f = \frac{1}{7}(g + h - k)$ .
2. We need to solve for $g$ .
3. The variables $h$ and $k$ are constants or known values.
4. The variable $f$ is a known value or constant.

STEP 2

First, we want to isolate the term containing $g$ on one side of the equation. To do this, we can start by multiplying both sides of the equation by 7 to eliminate the fraction.
$7 \cdot f = 7 \cdot \frac{1}{7}(g + h - k)$

STEP 3

Simplify both sides of the equation by performing the multiplication on the right side and canceling out the 7 in the denominator.
$7f = g + h - k$

STEP 4

Next, we want to isolate $g$ by moving the terms $h$ and $-k$ to the other side of the equation. We can do this by adding $k$ to both sides and subtracting $h$ from both sides.
$7f + h - k = g + h - k + h - k$

STEP 5

Simplify the equation by combining like terms.
$7f + h - k = g$

STEP 6

Now we have isolated $g$ on one side of the equation. The expression $7f + h - k$ is equal to $g$ .
$g = 7f + h - k$
So, the solution for $g$ is:
$g = 7f + h - k$

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Solve for ggg given the equation f=17(g+h−k)f=\frac{1}{7}(g+h-k)f=71​(g+h−k).

STEP 1

Assumptions1. The given equation is f=17(g+h−k) f = \frac{1}{7}(g + h - k) f=71​(g+h−k).2. We need to solve for g g g.3. The variables h h h and k k k are constants or known values.4. The variable f f f is a known value or constant.

STEP 2

First, we want to isolate the term containing g g g on one side of the equation. To do this, we can start by multiplying both sides of the equation by 7 to eliminate the fraction.7⋅f=7⋅17(g+h−k) 7 \cdot f = 7 \cdot \frac{1}{7}(g + h - k) 7⋅f=7⋅71​(g+h−k)

STEP 3

Simplify both sides of the equation by performing the multiplication on the right side and canceling out the 7 in the denominator.7f=g+h−k 7f = g + h - k 7f=g+h−k

STEP 4

Next, we want to isolate g g g by moving the terms h h h and −k -k −k to the other side of the equation. We can do this by adding k k k to both sides and subtracting h h h from both sides.7f+h−k=g+h−k+h−k 7f + h - k = g + h - k + h - k 7f+h−k=g+h−k+h−k

STEP 5

Simplify the equation by combining like terms.7f+h−k=g 7f + h - k = g 7f+h−k=g

STEP 6

Now we have isolated g g g on one side of the equation. The expression 7f+h−k 7f + h - k 7f+h−k is equal to g g g.g=7f+h−k g = 7f + h - k g=7f+h−kSo, the solution for g g g is:g=7f+h−k g = 7f + h - k g=7f+h−k

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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 $g$ given the equation $f=\frac{1}{7}(g+h-k)$ .

Assumptions
1. The given equation is $f = \frac{1}{7}(g + h - k)$ .
2. We need to solve for $g$ .
3. The variables $h$ and $k$ are constants or known values.
4. The variable $f$ is a known value or constant.

First, we want to isolate the term containing $g$ on one side of the equation. To do this, we can start by multiplying both sides of the equation by 7 to eliminate the fraction.
$7 \cdot f = 7 \cdot \frac{1}{7}(g + h - k)$

Simplify both sides of the equation by performing the multiplication on the right side and canceling out the 7 in the denominator.
$7f = g + h - k$

Next, we want to isolate $g$ by moving the terms $h$ and $-k$ to the other side of the equation. We can do this by adding $k$ to both sides and subtracting $h$ from both sides.
$7f + h - k = g + h - k + h - k$

Simplify the equation by combining like terms.
$7f + h - k = g$

Now we have isolated $g$ on one side of the equation. The expression $7f + h - k$ is equal to $g$ .
$g = 7f + h - k$
So, the solution for $g$ is:
$g = 7f + h - k$