Finite Math Examples

$| 1 - 4 t | + 3 = 20$

Step 1

Move all terms not containing $| 1 - 4 t |$ to the right side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

$| 1 - 4 t | = 20 - 3$

Step 1.2

Subtract $3$ from $20$ .

$| 1 - 4 t | = 17$

Step 2

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

$1 - 4 t = \pm 17$

Step 3

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

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Step 3.1

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

$1 - 4 t = 17$

Step 3.2

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

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Step 3.2.1

Subtract $1$ from both sides of the equation.

$- 4 t = 17 - 1$

Step 3.2.2

Subtract $1$ from $17$ .

$- 4 t = 16$

Step 3.3

Divide each term in $- 4 t = 16$ by $- 4$ and simplify.

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Step 3.3.1

Divide each term in $- 4 t = 16$ by $- 4$ .

$\frac{- 4 t}{- 4} = \frac{16}{- 4}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 4$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 4 t}{- 4} = \frac{16}{- 4}$

Step 3.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{16}{- 4}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $16$ by $- 4$ .

$t = - 4$

Step 3.4

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

$1 - 4 t = - 17$

Step 3.5

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

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Step 3.5.1

Subtract $1$ from both sides of the equation.

$- 4 t = - 17 - 1$

Step 3.5.2

Subtract $1$ from $- 17$ .

$- 4 t = - 18$

Step 3.6

Divide each term in $- 4 t = - 18$ by $- 4$ and simplify.

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Step 3.6.1

Divide each term in $- 4 t = - 18$ by $- 4$ .

$\frac{- 4 t}{- 4} = \frac{- 18}{- 4}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $- 4$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{- 4 t}{- 4} = \frac{- 18}{- 4}$

Step 3.6.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 18}{- 4}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Cancel the common factor of $- 18$ and $- 4$ .

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Step 3.6.3.1.1

Factor $- 2$ out of $- 18$ .

$t = \frac{- 2 (9)}{- 4}$

Step 3.6.3.1.2

Cancel the common factors.

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Step 3.6.3.1.2.1

Factor $- 2$ out of $- 4$ .

$t = \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Step 3.6.3.1.2.2

Cancel the common factor.

$t = \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Step 3.6.3.1.2.3

Rewrite the expression.

$t = \frac{9}{2}$

Step 3.7

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

$t = - 4, \frac{9}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = - 4, \frac{9}{2}$

Decimal Form:

$t = - 4, 4.5$

Mixed Number Form:

$t = - 4, 4 \frac{1}{2}$