Finite Math Examples

$| 2 k - 7 | + 4 = 11$

Step 1

Move all terms not containing $| 2 k - 7 |$ to the right side of the equation.

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Step 1.1

Subtract $4$ from both sides of the equation.

$| 2 k - 7 | = 11 - 4$

Step 1.2

Subtract $4$ from $11$ .

$| 2 k - 7 | = 7$

Step 2

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

$2 k - 7 = \pm 7$

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.

$2 k - 7 = 7$

Step 3.2

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

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Step 3.2.1

Add $7$ to both sides of the equation.

$2 k = 7 + 7$

Step 3.2.2

Add $7$ and $7$ .

$2 k = 14$

Step 3.3

Divide each term in $2 k = 14$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 k = 14$ by $2$ .

$\frac{2 k}{2} = \frac{14}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 k}{2} = \frac{14}{2}$

Step 3.3.2.1.2

Divide $k$ by $1$ .

$k = \frac{14}{2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $14$ by $2$ .

$k = 7$

Step 3.4

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

$2 k - 7 = - 7$

Step 3.5

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

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Step 3.5.1

Add $7$ to both sides of the equation.

$2 k = - 7 + 7$

Step 3.5.2

Add $- 7$ and $7$ .

$2 k = 0$

Step 3.6

Divide each term in $2 k = 0$ by $2$ and simplify.

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Step 3.6.1

Divide each term in $2 k = 0$ by $2$ .

$\frac{2 k}{2} = \frac{0}{2}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $2$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{2 k}{2} = \frac{0}{2}$

Step 3.6.2.1.2

Divide $k$ by $1$ .

$k = \frac{0}{2}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $0$ by $2$ .

$k = 0$

Step 3.7

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

$k = 7, 0$