Basic Math Examples

$7 k = \frac{4 k}{3 t} - 11 t$

Step 1

Subtract $\frac{4 k}{3 t}$ from both sides of the equation.

$7 k - \frac{4 k}{3 t} = - 11 t$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, 3 t, 1$

Step 2.2

The LCM of one and any expression is the expression.

$3 t$

Step 3

Multiply each term in $7 k - \frac{4 k}{3 t} = - 11 t$ by $3 t$ to eliminate the fractions.

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Step 3.1

Multiply each term in $7 k - \frac{4 k}{3 t} = - 11 t$ by $3 t$ .

$7 k (3 t) - \frac{4 k}{3 t} (3 t) = - 11 t (3 t)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$7 \cdot 3 k t - \frac{4 k}{3 t} (3 t) = - 11 t (3 t)$

Step 3.2.1.2

Multiply $7$ by $3$ .

$21 k t - \frac{4 k}{3 t} (3 t) = - 11 t (3 t)$

Step 3.2.1.3

Cancel the common factor of $3 t$ .

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Step 3.2.1.3.1

Move the leading negative in $- \frac{4 k}{3 t}$ into the numerator.

$21 k t + \frac{- 4 k}{3 t} (3 t) = - 11 t (3 t)$

Step 3.2.1.3.2

Cancel the common factor.

$21 k t + \frac{- 4 k}{3 t} (3 t) = - 11 t (3 t)$

Step 3.2.1.3.3

Rewrite the expression.

$21 k t - 4 k = - 11 t (3 t)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite using the commutative property of multiplication.

$21 k t - 4 k = - 11 \cdot 3 t \cdot t$

Step 3.3.2

Multiply $t$ by $t$ by adding the exponents.

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Step 3.3.2.1

Move $t$ .

$21 k t - 4 k = - 11 \cdot 3 (t \cdot t)$

Step 3.3.2.2

Multiply $t$ by $t$ .

$21 k t - 4 k = - 11 \cdot 3 t^{2}$

Step 3.3.3

Multiply $- 11$ by $3$ .

$21 k t - 4 k = - 33 t^{2}$

Step 4

Solve the equation.

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Step 4.1

Factor $k$ out of $21 k t - 4 k$ .

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Step 4.1.1

Factor $k$ out of $21 k t$ .

$k (21 t) - 4 k = - 33 t^{2}$

Step 4.1.2

Factor $k$ out of $- 4 k$ .

$k (21 t) + k \cdot - 4 = - 33 t^{2}$

Step 4.1.3

Factor $k$ out of $k (21 t) + k \cdot - 4$ .

$k (21 t - 4) = - 33 t^{2}$

Step 4.2

Divide each term in $k (21 t - 4) = - 33 t^{2}$ by $21 t - 4$ and simplify.

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Step 4.2.1

Divide each term in $k (21 t - 4) = - 33 t^{2}$ by $21 t - 4$ .

$\frac{k (21 t - 4)}{21 t - 4} = \frac{- 33 t^{2}}{21 t - 4}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $21 t - 4$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{k (21 t - 4)}{21 t - 4} = \frac{- 33 t^{2}}{21 t - 4}$

Step 4.2.2.1.2

Divide $k$ by $1$ .

$k = \frac{- 33 t^{2}}{21 t - 4}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$k = - \frac{33 t^{2}}{21 t - 4}$