Basic Math Examples

$| 4 a + 6 | - 4 a = - 10$

Step 1

Add $4 a$ to both sides of the equation.

$| 4 a + 6 | = - 10 + 4 a$

Step 2

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

$4 a + 6 = \pm (- 10 + 4 a)$

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.

$4 a + 6 = - 10 + 4 a$

Step 3.2

Move all terms containing $a$ to the left side of the equation.

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Step 3.2.1

Subtract $4 a$ from both sides of the equation.

$4 a + 6 - 4 a = - 10$

Step 3.2.2

Combine the opposite terms in $4 a + 6 - 4 a$ .

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Step 3.2.2.1

Subtract $4 a$ from $4 a$ .

$0 + 6 = - 10$

Step 3.2.2.2

Add $0$ and $6$ .

$6 = - 10$

Step 3.3

Since $6 \neq - 10$ , there are no solutions.

No solution

Step 3.4

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

$4 a + 6 = - (- 10 + 4 a)$

Step 3.5

Simplify $- (- 10 + 4 a)$ .

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Step 3.5.1

Rewrite.

$4 a + 6 = 0 + 0 - (- 10 + 4 a)$

Step 3.5.2

Simplify by adding zeros.

$4 a + 6 = - (- 10 + 4 a)$

Step 3.5.3

Apply the distributive property.

$4 a + 6 = - - 10 - (4 a)$

Step 3.5.4

Multiply.

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Step 3.5.4.1

Multiply $- 1$ by $- 10$ .

$4 a + 6 = 10 - (4 a)$

Step 3.5.4.2

Multiply $4$ by $- 1$ .

$4 a + 6 = 10 - 4 a$

Step 3.6

Move all terms containing $a$ to the left side of the equation.

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Step 3.6.1

Add $4 a$ to both sides of the equation.

$4 a + 6 + 4 a = 10$

Step 3.6.2

Add $4 a$ and $4 a$ .

$8 a + 6 = 10$

Step 3.7

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

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Step 3.7.1

Subtract $6$ from both sides of the equation.

$8 a = 10 - 6$

Step 3.7.2

Subtract $6$ from $10$ .

$8 a = 4$

Step 3.8

Divide each term in $8 a = 4$ by $8$ and simplify.

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Step 3.8.1

Divide each term in $8 a = 4$ by $8$ .

$\frac{8 a}{8} = \frac{4}{8}$

Step 3.8.2

Simplify the left side.

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Step 3.8.2.1

Cancel the common factor of $8$ .

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Step 3.8.2.1.1

Cancel the common factor.

$\frac{8 a}{8} = \frac{4}{8}$

Step 3.8.2.1.2

Divide $a$ by $1$ .

$a = \frac{4}{8}$

Step 3.8.3

Simplify the right side.

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Step 3.8.3.1

Cancel the common factor of $4$ and $8$ .

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Step 3.8.3.1.1

Factor $4$ out of $4$ .

$a = \frac{4 (1)}{8}$

Step 3.8.3.1.2

Cancel the common factors.

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Step 3.8.3.1.2.1

Factor $4$ out of $8$ .

$a = \frac{4 \cdot 1}{4 \cdot 2}$

Step 3.8.3.1.2.2

Cancel the common factor.

$a = \frac{4 \cdot 1}{4 \cdot 2}$

Step 3.8.3.1.2.3

Rewrite the expression.

$a = \frac{1}{2}$

Step 3.9

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

$a =$