Algebra Examples

$54 - \frac{1}{7} y i = 9 x - 4 i$

Step 1

Multiply $- \frac{1}{7} (y i)$ .

Tap for more steps...

Step 1.1

Combine $y$ and $\frac{1}{7}$ .

$54 - \frac{y}{7} i = 9 x - 4 i$

Step 1.2

Combine $i$ and $\frac{y}{7}$ .

$54 - \frac{i y}{7} = 9 x - 4 i$

Step 2

Subtract $54$ from both sides of the equation.

$- \frac{i y}{7} = 9 x - 4 i - 54$

Step 3

Multiply both sides of the equation by $- \frac{7}{i}$ .

$- \frac{7}{i} (- \frac{i y}{7}) = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $- \frac{7}{i} (- \frac{i y}{7})$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.1.1.1.1

Move the leading negative in $- \frac{7}{i}$ into the numerator.

$\frac{- 7}{i} (- \frac{i y}{7}) = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.1.2

Move the leading negative in $- \frac{i y}{7}$ into the numerator.

$\frac{- 7}{i} \cdot \frac{- i y}{7} = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{i} \cdot \frac{- i y}{7} = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{i} \cdot \frac{- i y}{7} = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{i} (- i y) = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.2

Cancel the common factor of $i$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $i$ out of $- i y$ .

$\frac{- 1}{i} (i (- y)) = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{i} (i (- y)) = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.2.3

Rewrite the expression.

$- - y = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.3

Multiply.

Tap for more steps...

Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{7}{i} (9 x - 4 i - 54)$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- \frac{7}{i} (9 x - 4 i - 54)$ .

Tap for more steps...

Step 4.2.1.1

Multiply the numerator and denominator of $\frac{7}{i}$ by the conjugate of $i$ to make the denominator real.

$y = - (\frac{7}{i} \cdot \frac{i}{i}) (9 x - 4 i - 54)$

Step 4.2.1.2

Multiply.

Tap for more steps...

Step 4.2.1.2.1

Combine.

$y = - \frac{7 i}{i i} (9 x - 4 i - 54)$

Step 4.2.1.2.2

Simplify the denominator.

Tap for more steps...

Step 4.2.1.2.2.1

Raise $i$ to the power of $1$ .

$y = - \frac{7 i}{i^{1} i} (9 x - 4 i - 54)$

Step 4.2.1.2.2.2

Raise $i$ to the power of $1$ .

$y = - \frac{7 i}{i^{1} i^{1}} (9 x - 4 i - 54)$

Step 4.2.1.2.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - \frac{7 i}{i^{1 + 1}} (9 x - 4 i - 54)$

Step 4.2.1.2.2.4

Add $1$ and $1$ .

$y = - \frac{7 i}{i^{2}} (9 x - 4 i - 54)$

Step 4.2.1.2.2.5

Rewrite $i^{2}$ as $- 1$ .

$y = - \frac{7 i}{- 1} (9 x - 4 i - 54)$

Step 4.2.1.3

Simplify the expression.

Tap for more steps...

Step 4.2.1.3.1

Move the negative one from the denominator of $\frac{7 i}{- 1}$ .

$y = - (- 1 \cdot (7 i)) (9 x - 4 i - 54)$

Step 4.2.1.3.2

Rewrite $- 1 \cdot (7 i)$ as $- (7 i)$ .

$y = - - (7 i) (9 x - 4 i - 54)$

Step 4.2.1.3.3

Multiply $7$ by $- 1$ .

$y = - (- 7 i) (9 x - 4 i - 54)$

Step 4.2.1.3.4

Multiply $- 7$ by $- 1$ .

$y = 7 i (9 x - 4 i - 54)$

Step 4.2.1.4

Apply the distributive property.

$y = 7 i (9 x) + 7 i (- 4 i) + 7 i \cdot - 54$

Step 4.2.1.5

Simplify.

Tap for more steps...

Step 4.2.1.5.1

Multiply $9$ by $7$ .

$y = 63 i x + 7 i (- 4 i) + 7 i \cdot - 54$

Step 4.2.1.5.2

Multiply $7 i (- 4 i)$ .

Tap for more steps...

Step 4.2.1.5.2.1

Multiply $- 4$ by $7$ .

$y = 63 i x - 28 i i + 7 i \cdot - 54$

Step 4.2.1.5.2.2

Raise $i$ to the power of $1$ .

$y = 63 i x - 28 (i^{1} i) + 7 i \cdot - 54$

Step 4.2.1.5.2.3

Raise $i$ to the power of $1$ .

$y = 63 i x - 28 (i^{1} i^{1}) + 7 i \cdot - 54$

Step 4.2.1.5.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 63 i x - 28 i^{1 + 1} + 7 i \cdot - 54$

Step 4.2.1.5.2.5

Add $1$ and $1$ .

$y = 63 i x - 28 i^{2} + 7 i \cdot - 54$

Step 4.2.1.5.3

Multiply $- 54$ by $7$ .

$y = 63 i x - 28 i^{2} - 378 i$

Step 4.2.1.6

Simplify each term.

Tap for more steps...

Step 4.2.1.6.1

Rewrite $i^{2}$ as $- 1$ .

$y = 63 i x - 28 \cdot - 1 - 378 i$

Step 4.2.1.6.2

Multiply $- 28$ by $- 1$ .

$y = 63 i x + 28 - 378 i$

Step 5

Move $i$ .

$y = 63 x i + 28 - 378 i$