Basic Math Examples

$\frac{4 a - 35}{3} = (9 - a)$

Step 1

Multiply both sides by $3$ .

$\frac{4 a - 35}{3} \cdot 3 = (9 - a) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{4 a - 35}{3} \cdot 3 = (9 - a) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$4 a - 35 = (9 - a) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(9 - a) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$4 a - 35 = 9 \cdot 3 - a \cdot 3$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Multiply $9$ by $3$ .

$4 a - 35 = 27 - a \cdot 3$

Step 2.2.1.2.2

Multiply $3$ by $- 1$ .

$4 a - 35 = 27 - 3 a$

Step 2.2.1.2.3

Reorder $27$ and $- 3 a$ .

$4 a - 35 = - 3 a + 27$

Step 3

Solve for $a$ .

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Step 3.1

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

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Step 3.1.1

Add $3 a$ to both sides of the equation.

$4 a - 35 + 3 a = 27$

Step 3.1.2

Add $4 a$ and $3 a$ .

$7 a - 35 = 27$

Step 3.2

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

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Step 3.2.1

Add $35$ to both sides of the equation.

$7 a = 27 + 35$

Step 3.2.2

Add $27$ and $35$ .

$7 a = 62$

Step 3.3

Divide each term in $7 a = 62$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 a = 62$ by $7$ .

$\frac{7 a}{7} = \frac{62}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 a}{7} = \frac{62}{7}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{62}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{62}{7}$

Decimal Form:

$a = 8.\overline{857142}$

Mixed Number Form:

$a = 8 \frac{6}{7}$