Basic Math Examples

$3 a + 2 (5 a - 5) = 2 (3 a + 4)$

Step 1

Simplify $3 a + 2 (5 a - 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 a + 2 (5 a) + 2 \cdot - 5 = 2 (3 a + 4)$

Step 1.1.2

Multiply $5$ by $2$ .

$3 a + 10 a + 2 \cdot - 5 = 2 (3 a + 4)$

Step 1.1.3

Multiply $2$ by $- 5$ .

$3 a + 10 a - 10 = 2 (3 a + 4)$

Step 1.2

Add $3 a$ and $10 a$ .

$13 a - 10 = 2 (3 a + 4)$

Step 2

Simplify $2 (3 a + 4)$ .

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Step 2.1

Apply the distributive property.

$13 a - 10 = 2 (3 a) + 2 \cdot 4$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $2$ .

$13 a - 10 = 6 a + 2 \cdot 4$

Step 2.2.2

Multiply $2$ by $4$ .

$13 a - 10 = 6 a + 8$

Step 3

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

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Step 3.1

Subtract $6 a$ from both sides of the equation.

$13 a - 10 - 6 a = 8$

Step 3.2

Subtract $6 a$ from $13 a$ .

$7 a - 10 = 8$

Step 4

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

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Step 4.1

Add $10$ to both sides of the equation.

$7 a = 8 + 10$

Step 4.2

Add $8$ and $10$ .

$7 a = 18$

Step 5

Divide each term in $7 a = 18$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 a = 18$ by $7$ .

$\frac{7 a}{7} = \frac{18}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 a}{7} = \frac{18}{7}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{18}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{18}{7}$

Decimal Form:

$a = 2.\overline{571428}$

Mixed Number Form:

$a = 2 \frac{4}{7}$