Basic Math Examples

$- 3 (2 a - 5) + 6 a = 18 a + 1$

Step 1

Simplify $- 3 (2 a - 5) + 6 a$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 3 (2 a) - 3 \cdot - 5 + 6 a = 18 a + 1$

Step 1.1.2

Multiply $2$ by $- 3$ .

$- 6 a - 3 \cdot - 5 + 6 a = 18 a + 1$

Step 1.1.3

Multiply $- 3$ by $- 5$ .

$- 6 a + 15 + 6 a = 18 a + 1$

Step 1.2

Combine the opposite terms in $- 6 a + 15 + 6 a$ .

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Step 1.2.1

Add $- 6 a$ and $6 a$ .

$0 + 15 = 18 a + 1$

Step 1.2.2

Add $0$ and $15$ .

$15 = 18 a + 1$

Step 2

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$18 a + 1 = 15$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$18 a = 15 - 1$

Step 3.2

Subtract $1$ from $15$ .

$18 a = 14$

Step 4

Divide each term in $18 a = 14$ by $18$ and simplify.

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Step 4.1

Divide each term in $18 a = 14$ by $18$ .

$\frac{18 a}{18} = \frac{14}{18}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $18$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{18 a}{18} = \frac{14}{18}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{14}{18}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $14$ and $18$ .

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Step 4.3.1.1

Factor $2$ out of $14$ .

$a = \frac{2 (7)}{18}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $18$ .

$a = \frac{2 \cdot 7}{2 \cdot 9}$

Step 4.3.1.2.2

Cancel the common factor.

$a = \frac{2 \cdot 7}{2 \cdot 9}$

Step 4.3.1.2.3

Rewrite the expression.

$a = \frac{7}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{7}{9}$

Decimal Form:

$a = 0.\overline{7}$