Finite Math Examples

$| t - \frac{3}{2} | = \frac{5}{2}$

Step 1

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

$t - \frac{3}{2} = \pm \frac{5}{2}$

Step 2

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

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Step 2.1

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

$t - \frac{3}{2} = \frac{5}{2}$

Step 2.2

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

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Step 2.2.1

Add $\frac{3}{2}$ to both sides of the equation.

$t = \frac{5}{2} + \frac{3}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$t = \frac{5 + 3}{2}$

Step 2.2.3

Add $5$ and $3$ .

$t = \frac{8}{2}$

Step 2.2.4

Divide $8$ by $2$ .

$t = 4$

Step 2.3

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

$t - \frac{3}{2} = - \frac{5}{2}$

Step 2.4

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

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Step 2.4.1

Add $\frac{3}{2}$ to both sides of the equation.

$t = - \frac{5}{2} + \frac{3}{2}$

Step 2.4.2

Combine the numerators over the common denominator.

$t = \frac{- 5 + 3}{2}$

Step 2.4.3

Add $- 5$ and $3$ .

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

Step 2.4.4

Divide $- 2$ by $2$ .

$t = - 1$

Step 2.5

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

$t = 4, - 1$