Basic Math Examples

$2 a + \frac{5 a - 10}{24} = 1 - \frac{2 a - 13}{3}$

Step 1

Simplify $2 a + \frac{5 a - 10}{24}$ .

Tap for more steps...

Step 1.1

Factor $5$ out of $5 a - 10$ .

Tap for more steps...

Step 1.1.1

Factor $5$ out of $5 a$ .

$2 a + \frac{5 (a) - 10}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.1.2

Factor $5$ out of $- 10$ .

$2 a + \frac{5 a + 5 \cdot - 2}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.1.3

Factor $5$ out of $5 a + 5 \cdot - 2$ .

$2 a + \frac{5 (a - 2)}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.2

To write $2 a$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$2 a \cdot \frac{24}{24} + \frac{5 (a - 2)}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.3

Simplify terms.

Tap for more steps...

Step 1.3.1

Combine $2 a$ and $\frac{24}{24}$ .

$\frac{2 a \cdot 24}{24} + \frac{5 (a - 2)}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{2 a \cdot 24 + 5 (a - 2)}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.4

Simplify the numerator.

Tap for more steps...

Step 1.4.1

Multiply $24$ by $2$ .

$\frac{48 a + 5 (a - 2)}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.4.2

Apply the distributive property.

$\frac{48 a + 5 a + 5 \cdot - 2}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.4.3

Multiply $5$ by $- 2$ .

$\frac{48 a + 5 a - 10}{24} = 1 - \frac{2 a - 13}{3}$

Step 1.4.4

Add $48 a$ and $5 a$ .

$\frac{53 a - 10}{24} = 1 - \frac{2 a - 13}{3}$

Step 2

Simplify $1 - \frac{2 a - 13}{3}$ .

Tap for more steps...

Step 2.1

Combine into one fraction.

Tap for more steps...

Step 2.1.1

Write $1$ as a fraction with a common denominator.

$\frac{53 a - 10}{24} = \frac{3}{3} - \frac{2 a - 13}{3}$

Step 2.1.2

Combine the numerators over the common denominator.

$\frac{53 a - 10}{24} = \frac{3 - (2 a - 13)}{3}$

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

$\frac{53 a - 10}{24} = \frac{3 - (2 a) - - 13}{3}$

Step 2.2.2

Multiply $2$ by $- 1$ .

$\frac{53 a - 10}{24} = \frac{3 - 2 a - - 13}{3}$

Step 2.2.3

Multiply $- 1$ by $- 13$ .

$\frac{53 a - 10}{24} = \frac{3 - 2 a + 13}{3}$

Step 2.2.4

Add $3$ and $13$ .

$\frac{53 a - 10}{24} = \frac{- 2 a + 16}{3}$

Step 2.2.5

Factor $2$ out of $- 2 a + 16$ .

Tap for more steps...

Step 2.2.5.1

Factor $2$ out of $- 2 a$ .

$\frac{53 a - 10}{24} = \frac{2 (- a) + 16}{3}$

Step 2.2.5.2

Factor $2$ out of $16$ .

$\frac{53 a - 10}{24} = \frac{2 (- a) + 2 (8)}{3}$

Step 2.2.5.3

Factor $2$ out of $2 (- a) + 2 (8)$ .

$\frac{53 a - 10}{24} = \frac{2 (- a + 8)}{3}$

Step 2.3

Simplify with factoring out.

Tap for more steps...

Step 2.3.1

Factor $- 1$ out of $- a$ .

$\frac{53 a - 10}{24} = \frac{2 (- (a) + 8)}{3}$

Step 2.3.2

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{53 a - 10}{24} = \frac{2 (- (a) - 1 (- 8))}{3}$

Step 2.3.3

Factor $- 1$ out of $- (a) - 1 (- 8)$ .

$\frac{53 a - 10}{24} = \frac{2 (- (a - 8))}{3}$

Step 2.3.4

Simplify the expression.

Tap for more steps...

Step 2.3.4.1

Rewrite $- (a - 8)$ as $- 1 (a - 8)$ .

$\frac{53 a - 10}{24} = \frac{2 (- 1 (a - 8))}{3}$

Step 2.3.4.2

Move the negative in front of the fraction.

$\frac{53 a - 10}{24} = - \frac{2 (a - 8)}{3}$

Step 3

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

Tap for more steps...

Step 3.1

Add $\frac{2 (a - 8)}{3}$ to both sides of the equation.

$\frac{53 a - 10}{24} + \frac{2 (a - 8)}{3} = 0$

Step 3.2

To write $\frac{2 (a - 8)}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{53 a - 10}{24} + \frac{2 (a - 8)}{3} \cdot \frac{8}{8} = 0$

Step 3.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{2 (a - 8)}{3}$ by $\frac{8}{8}$ .

$\frac{53 a - 10}{24} + \frac{2 (a - 8) \cdot 8}{3 \cdot 8} = 0$

Step 3.3.2

Multiply $3$ by $8$ .

$\frac{53 a - 10}{24} + \frac{2 (a - 8) \cdot 8}{24} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{53 a - 10 + 2 (a - 8) \cdot 8}{24} = 0$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Apply the distributive property.

$\frac{53 a - 10 + (2 a + 2 \cdot - 8) \cdot 8}{24} = 0$

Step 3.5.2

Multiply $2$ by $- 8$ .

$\frac{53 a - 10 + (2 a - 16) \cdot 8}{24} = 0$

Step 3.5.3

Apply the distributive property.

$\frac{53 a - 10 + 2 a \cdot 8 - 16 \cdot 8}{24} = 0$

Step 3.5.4

Multiply $8$ by $2$ .

$\frac{53 a - 10 + 16 a - 16 \cdot 8}{24} = 0$

Step 3.5.5

Multiply $- 16$ by $8$ .

$\frac{53 a - 10 + 16 a - 128}{24} = 0$

Step 3.5.6

Add $53 a$ and $16 a$ .

$\frac{69 a - 10 - 128}{24} = 0$

Step 3.5.7

Subtract $128$ from $- 10$ .

$\frac{69 a - 138}{24} = 0$

Step 3.5.8

Factor $69$ out of $69 a - 138$ .

Tap for more steps...

Step 3.5.8.1

Factor $69$ out of $69 a$ .

$\frac{69 (a) - 138}{24} = 0$

Step 3.5.8.2

Factor $69$ out of $- 138$ .

$\frac{69 a + 69 \cdot - 2}{24} = 0$

Step 3.5.8.3

Factor $69$ out of $69 a + 69 \cdot - 2$ .

$\frac{69 (a - 2)}{24} = 0$

Step 3.6

Cancel the common factor of $69$ and $24$ .

Tap for more steps...

Step 3.6.1

Factor $3$ out of $69 (a - 2)$ .

$\frac{3 (23 (a - 2))}{24} = 0$

Step 3.6.2

Cancel the common factors.

Tap for more steps...

Step 3.6.2.1

Factor $3$ out of $24$ .

$\frac{3 (23 (a - 2))}{3 (8)} = 0$

Step 3.6.2.2

Cancel the common factor.

$\frac{3 (23 (a - 2))}{3 \cdot 8} = 0$

Step 3.6.2.3

Rewrite the expression.

$\frac{23 (a - 2)}{8} = 0$

Step 4

Set the numerator equal to zero.

$23 (a - 2) = 0$

Step 5

Solve the equation for $a$ .

Tap for more steps...

Step 5.1

Divide each term in $23 (a - 2) = 0$ by $23$ and simplify.

Tap for more steps...

Step 5.1.1

Divide each term in $23 (a - 2) = 0$ by $23$ .

$\frac{23 (a - 2)}{23} = \frac{0}{23}$

Step 5.1.2

Simplify the left side.

Tap for more steps...

Step 5.1.2.1

Cancel the common factor of $23$ .

Tap for more steps...

Step 5.1.2.1.1

Cancel the common factor.

$\frac{23 (a - 2)}{23} = \frac{0}{23}$

Step 5.1.2.1.2

Divide $a - 2$ by $1$ .

$a - 2 = \frac{0}{23}$

Step 5.1.3

Simplify the right side.

Tap for more steps...

Step 5.1.3.1

Divide $0$ by $23$ .

$a - 2 = 0$

Step 5.2

Add $2$ to both sides of the equation.

$a = 2$