Algebra Examples

$d = | 300 - 48 t |$

Step 1

Rewrite the equation as $| 300 - 48 t | = d$ .

$| 300 - 48 t | = d$

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$300 - 48 t = \pm d$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$300 - 48 t = d$

Step 3.2

Subtract $300$ from both sides of the equation.

$- 48 t = d - 300$

Step 3.3

Divide each term in $- 48 t = d - 300$ by $- 48$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 48 t = d - 300$ by $- 48$ .

$\frac{- 48 t}{- 48} = \frac{d}{- 48} + \frac{- 300}{- 48}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 48$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 48 t}{- 48} = \frac{d}{- 48} + \frac{- 300}{- 48}$

Step 3.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{d}{- 48} + \frac{- 300}{- 48}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.3.1.1

Move the negative in front of the fraction.

$t = - \frac{d}{48} + \frac{- 300}{- 48}$

Step 3.3.3.1.2

Cancel the common factor of $- 300$ and $- 48$ .

Tap for more steps...

Step 3.3.3.1.2.1

Factor $- 12$ out of $- 300$ .

$t = - \frac{d}{48} + \frac{- 12 (25)}{- 48}$

Step 3.3.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 3.3.3.1.2.2.1

Factor $- 12$ out of $- 48$ .

$t = - \frac{d}{48} + \frac{- 12 \cdot 25}{- 12 \cdot 4}$

Step 3.3.3.1.2.2.2

Cancel the common factor.

$t = - \frac{d}{48} + \frac{- 12 \cdot 25}{- 12 \cdot 4}$

Step 3.3.3.1.2.2.3

Rewrite the expression.

$t = - \frac{d}{48} + \frac{25}{4}$

Step 3.4

Next, use the negative value of the $\pm$ to find the second solution.

$300 - 48 t = - d$

Step 3.5

Subtract $300$ from both sides of the equation.

$- 48 t = - d - 300$

Step 3.6

Divide each term in $- 48 t = - d - 300$ by $- 48$ and simplify.

Tap for more steps...

Step 3.6.1

Divide each term in $- 48 t = - d - 300$ by $- 48$ .

$\frac{- 48 t}{- 48} = \frac{- d}{- 48} + \frac{- 300}{- 48}$

Step 3.6.2

Simplify the left side.

Tap for more steps...

Step 3.6.2.1

Cancel the common factor of $- 48$ .

Tap for more steps...

Step 3.6.2.1.1

Cancel the common factor.

$\frac{- 48 t}{- 48} = \frac{- d}{- 48} + \frac{- 300}{- 48}$

Step 3.6.2.1.2

Divide $t$ by $1$ .

$t = \frac{- d}{- 48} + \frac{- 300}{- 48}$

Step 3.6.3

Simplify the right side.

Tap for more steps...

Step 3.6.3.1

Simplify each term.

Tap for more steps...

Step 3.6.3.1.1

Dividing two negative values results in a positive value.

$t = \frac{d}{48} + \frac{- 300}{- 48}$

Step 3.6.3.1.2

Cancel the common factor of $- 300$ and $- 48$ .

Tap for more steps...

Step 3.6.3.1.2.1

Factor $- 12$ out of $- 300$ .

$t = \frac{d}{48} + \frac{- 12 (25)}{- 48}$

Step 3.6.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 3.6.3.1.2.2.1

Factor $- 12$ out of $- 48$ .

$t = \frac{d}{48} + \frac{- 12 \cdot 25}{- 12 \cdot 4}$

Step 3.6.3.1.2.2.2

Cancel the common factor.

$t = \frac{d}{48} + \frac{- 12 \cdot 25}{- 12 \cdot 4}$

Step 3.6.3.1.2.2.3

Rewrite the expression.

$t = \frac{d}{48} + \frac{25}{4}$

Step 3.7

The complete solution is the result of both the positive and negative portions of the solution.

$t = - \frac{d}{48} + \frac{25}{4}$

$t = \frac{d}{48} + \frac{25}{4}$

$t = - \frac{d}{48} + \frac{25}{4}$

$t = \frac{d}{48} + \frac{25}{4}$