Basic Math Examples

$83 = j (7 + k) + c (2 k)$

Step 1

Rewrite the equation as $j (7 + k) + c \cdot (2 k) = 83$ .

$j (7 + k) + c \cdot (2 k) = 83$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$j \cdot 7 + j k + c \cdot (2 k) = 83$

Step 2.2

Move $7$ to the left of $j$ .

$7 \cdot j + j k + c \cdot (2 k) = 83$

Step 2.3

Rewrite using the commutative property of multiplication.

$7 j + j k + 2 c k = 83$

Step 3

Move all terms not containing $c$ to the right side of the equation.

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Step 3.1

Subtract $7 j$ from both sides of the equation.

$j k + 2 c k = 83 - 7 j$

Step 3.2

Subtract $j k$ from both sides of the equation.

$2 c k = 83 - 7 j - j k$

Step 4

Divide each term in $2 c k = 83 - 7 j - j k$ by $2 k$ and simplify.

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Step 4.1

Divide each term in $2 c k = 83 - 7 j - j k$ by $2 k$ .

$\frac{2 c k}{2 k} = \frac{83}{2 k} + \frac{- 7 j}{2 k} + \frac{- j k}{2 k}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 c k}{2 k} = \frac{83}{2 k} + \frac{- 7 j}{2 k} + \frac{- j k}{2 k}$

Step 4.2.1.2

Rewrite the expression.

$\frac{c k}{k} = \frac{83}{2 k} + \frac{- 7 j}{2 k} + \frac{- j k}{2 k}$

Step 4.2.2

Cancel the common factor of $k$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{c k}{k} = \frac{83}{2 k} + \frac{- 7 j}{2 k} + \frac{- j k}{2 k}$

Step 4.2.2.2

Divide $c$ by $1$ .

$c = \frac{83}{2 k} + \frac{- 7 j}{2 k} + \frac{- j k}{2 k}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative in front of the fraction.

$c = \frac{83}{2 k} - \frac{7 j}{2 k} + \frac{- j k}{2 k}$

Step 4.3.1.2

Cancel the common factor of $k$ .

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Step 4.3.1.2.1

Cancel the common factor.

$c = \frac{83}{2 k} - \frac{7 j}{2 k} + \frac{- j k}{2 k}$

Step 4.3.1.2.2

Rewrite the expression.

$c = \frac{83}{2 k} - \frac{7 j}{2 k} + \frac{- j}{2}$

Step 4.3.1.3

Move the negative in front of the fraction.

$c = \frac{83}{2 k} - \frac{7 j}{2 k} - \frac{j}{2}$