Basic Math Examples

$\frac{2 a - 5}{3 a} = - 2$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 a, 1$

Step 1.2

The LCM of one and any expression is the expression.

$3 a$

Step 2

Multiply each term in $\frac{2 a - 5}{3 a} = - 2$ by $3 a$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2 a - 5}{3 a} = - 2$ by $3 a$ .

$\frac{2 a - 5}{3 a} (3 a) = - 2 (3 a)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$3 \frac{2 a - 5}{3 a} a = - 2 (3 a)$

Step 2.2.2

Cancel the common factor of $3$ .

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Step 2.2.2.1

Factor $3$ out of $3 a$ .

$3 \frac{2 a - 5}{3 (a)} a = - 2 (3 a)$

Step 2.2.2.2

Cancel the common factor.

$3 \frac{2 a - 5}{3 a} a = - 2 (3 a)$

Step 2.2.2.3

Rewrite the expression.

$\frac{2 a - 5}{a} a = - 2 (3 a)$

Step 2.2.3

Cancel the common factor of $a$ .

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Step 2.2.3.1

Cancel the common factor.

$\frac{2 a - 5}{a} a = - 2 (3 a)$

Step 2.2.3.2

Rewrite the expression.

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $3$ by $- 2$ .

$2 a - 5 = - 6 a$

Step 3

Solve the equation.

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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 $6 a$ to both sides of the equation.

$2 a - 5 + 6 a = 0$

Step 3.1.2

Add $2 a$ and $6 a$ .

$8 a - 5 = 0$

Step 3.2

Add $5$ to both sides of the equation.

$8 a = 5$

Step 3.3

Divide each term in $8 a = 5$ by $8$ and simplify.

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Step 3.3.1

Divide each term in $8 a = 5$ by $8$ .

$\frac{8 a}{8} = \frac{5}{8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{8 a}{8} = \frac{5}{8}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{5}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{5}{8}$

Decimal Form:

$a = 0.625$