QuestionSolve for $C$ in the equation: $a(b - c) = d$ .

Studdy Solution

STEP 1

Assumptions1. $a$ , $b$ , $c$ , and $d$ are real numbers. . $a$ is not equal to zero.

STEP 2

We want to solve for $c$ , so we need to isolate $c$ on one side of the equation. First, we can divide both sides of the equation by $a$ to get rid of $a$ on the left side.
$\frac{a(b-c)}{a} = \frac{d}{a}$

STEP 3

implify the equation.
$b - c = \frac{d}{a}$

STEP 4

Now, we need to isolate $c$ . We can do this by subtracting $b$ from both sides of the equation.
$b - c - b = \frac{d}{a} - b$

STEP 5

implify the equation.
$-c = \frac{d}{a} - b$

STEP 6

To get rid of the negative sign in front of $c$ , we can multiply both sides of the equation by $-1$ .
$-1(-c) = -1\left(\frac{d}{a} - b\right)$

STEP 7

implify the equation.
$c = b - \frac{d}{a}$ So, the solution for $c$ is $c = b - \frac{d}{a}$ .

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QuestionSolve for $C$ in the equation: $a(b - c) = d$ .

Studdy Solution

STEP 1

Assumptions1. $a$ , $b$ , $c$ , and $d$ are real numbers. . $a$ is not equal to zero.

STEP 2

We want to solve for $c$ , so we need to isolate $c$ on one side of the equation. First, we can divide both sides of the equation by $a$ to get rid of $a$ on the left side.
$\frac{a(b-c)}{a} = \frac{d}{a}$

STEP 3

implify the equation.
$b - c = \frac{d}{a}$

STEP 4

Now, we need to isolate $c$ . We can do this by subtracting $b$ from both sides of the equation.
$b - c - b = \frac{d}{a} - b$

STEP 5

implify the equation.
$-c = \frac{d}{a} - b$

STEP 6

To get rid of the negative sign in front of $c$ , we can multiply both sides of the equation by $-1$ .
$-1(-c) = -1\left(\frac{d}{a} - b\right)$

STEP 7

implify the equation.
$c = b - \frac{d}{a}$ So, the solution for $c$ is $c = b - \frac{d}{a}$ .

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QuestionSolve for CCC in the equation: a(b−c)=da(b - c) = da(b−c)=d.

Studdy Solution

STEP 1

Assumptions1. aaa, bbb, ccc, and ddd are real numbers. . aaa is not equal to zero.

STEP 2

We want to solve for ccc, so we need to isolate ccc on one side of the equation. First, we can divide both sides of the equation by aaa to get rid of aaa on the left side.a(b−c)a=da\frac{a(b-c)}{a} = \frac{d}{a}aa(b−c)​=ad​

STEP 3

implify the equation.b−c=dab - c = \frac{d}{a}b−c=ad​

STEP 4

Now, we need to isolate ccc. We can do this by subtracting bbb from both sides of the equation.b−c−b=da−bb - c - b = \frac{d}{a} - bb−c−b=ad​−b

STEP 5

implify the equation.−c=da−b-c = \frac{d}{a} - b−c=ad​−b

STEP 6

To get rid of the negative sign in front of ccc, we can multiply both sides of the equation by −1-1−1.−1(−c)=−1(da−b)-1(-c) = -1\left(\frac{d}{a} - b\right)−1(−c)=−1(ad​−b)

STEP 7

implify the equation.c=b−dac = b - \frac{d}{a}c=b−ad​So, the solution for ccc is c=b−dac = b - \frac{d}{a}c=b−ad​.

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QuestionSolve for $C$ in the equation: $a(b - c) = d$ .

Assumptions1. $a$ , $b$ , $c$ , and $d$ are real numbers. . $a$ is not equal to zero.

We want to solve for $c$ , so we need to isolate $c$ on one side of the equation. First, we can divide both sides of the equation by $a$ to get rid of $a$ on the left side.
$\frac{a(b-c)}{a} = \frac{d}{a}$

implify the equation.
$b - c = \frac{d}{a}$

Now, we need to isolate $c$ . We can do this by subtracting $b$ from both sides of the equation.
$b - c - b = \frac{d}{a} - b$

implify the equation.
$-c = \frac{d}{a} - b$

To get rid of the negative sign in front of $c$ , we can multiply both sides of the equation by $-1$ .
$-1(-c) = -1\left(\frac{d}{a} - b\right)$

implify the equation.
$c = b - \frac{d}{a}$ So, the solution for $c$ is $c = b - \frac{d}{a}$ .