Basic Math Examples

$\frac{7}{4} \cdot | 3 j + 5 | + 1 = 15$

Step 1

Combine $\frac{7}{4}$ and $| 3 j + 5 |$ .

$\frac{7 | 3 j + 5 |}{4} + 1 = 15$

Step 2

Move all terms not containing $| 3 j + 5 |$ to the right side of the equation.

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Step 2.1

Subtract $1$ from both sides of the equation.

$\frac{7 | 3 j + 5 |}{4} = 15 - 1$

Step 2.2

Subtract $1$ from $15$ .

$\frac{7 | 3 j + 5 |}{4} = 14$

Step 3

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 | 3 j + 5 |}{4} = \frac{4}{7} \cdot 14$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{4}{7} \cdot \frac{7 | 3 j + 5 |}{4}$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 | 3 j + 5 |}{4} = \frac{4}{7} \cdot 14$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 | 3 j + 5 |) = \frac{4}{7} \cdot 14$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 | 3 j + 5 |$ .

$\frac{1}{7} (7 | 3 j + 5 |) = \frac{4}{7} \cdot 14$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 | 3 j + 5 |) = \frac{4}{7} \cdot 14$

Step 4.1.1.2.3

Rewrite the expression.

$| 3 j + 5 | = \frac{4}{7} \cdot 14$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{7} \cdot 14$ .

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Step 4.2.1.1

Cancel the common factor of $7$ .

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Step 4.2.1.1.1

Factor $7$ out of $14$ .

$| 3 j + 5 | = \frac{4}{7} \cdot (7 (2))$

Step 4.2.1.1.2

Cancel the common factor.

$| 3 j + 5 | = \frac{4}{7} \cdot (7 \cdot 2)$

Step 4.2.1.1.3

Rewrite the expression.

$| 3 j + 5 | = 4 \cdot 2$

Step 4.2.1.2

Multiply $4$ by $2$ .

$| 3 j + 5 | = 8$

Step 5

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

$3 j + 5 = \pm 8$

Step 6

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

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Step 6.1

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

$3 j + 5 = 8$

Step 6.2

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

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Step 6.2.1

Subtract $5$ from both sides of the equation.

$3 j = 8 - 5$

Step 6.2.2

Subtract $5$ from $8$ .

$3 j = 3$

Step 6.3

Divide each term in $3 j = 3$ by $3$ and simplify.

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Step 6.3.1

Divide each term in $3 j = 3$ by $3$ .

$\frac{3 j}{3} = \frac{3}{3}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $3$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{3 j}{3} = \frac{3}{3}$

Step 6.3.2.1.2

Divide $j$ by $1$ .

$j = \frac{3}{3}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Divide $3$ by $3$ .

$j = 1$

Step 6.4

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

$3 j + 5 = - 8$

Step 6.5

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

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Step 6.5.1

Subtract $5$ from both sides of the equation.

$3 j = - 8 - 5$

Step 6.5.2

Subtract $5$ from $- 8$ .

$3 j = - 13$

Step 6.6

Divide each term in $3 j = - 13$ by $3$ and simplify.

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Step 6.6.1

Divide each term in $3 j = - 13$ by $3$ .

$\frac{3 j}{3} = \frac{- 13}{3}$

Step 6.6.2

Simplify the left side.

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Step 6.6.2.1

Cancel the common factor of $3$ .

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Step 6.6.2.1.1

Cancel the common factor.

$\frac{3 j}{3} = \frac{- 13}{3}$

Step 6.6.2.1.2

Divide $j$ by $1$ .

$j = \frac{- 13}{3}$

Step 6.6.3

Simplify the right side.

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Step 6.6.3.1

Move the negative in front of the fraction.

$j = - \frac{13}{3}$

Step 6.7

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

$j = 1, - \frac{13}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$j = 1, - \frac{13}{3}$

Decimal Form:

$j = 1, - 4.\overline{3}$

Mixed Number Form:

$j = 1, - 4 \frac{1}{3}$