Linear Algebra Examples

$\frac{4 x - 3}{5} - \frac{2 x - 3}{2} = - 2$

Step 1

Simplify $\frac{4 x - 3}{5} - \frac{2 x - 3}{2}$ .

Tap for more steps...

Step 1.1

To write $\frac{4 x - 3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x - 3}{5} \cdot \frac{2}{2} - \frac{2 x - 3}{2} = - 2$

Step 1.2

To write $- \frac{2 x - 3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 x - 3}{5} \cdot \frac{2}{2} - \frac{2 x - 3}{2} \cdot \frac{5}{5} = - 2$

Step 1.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{4 x - 3}{5}$ by $\frac{2}{2}$ .

$\frac{(4 x - 3) \cdot 2}{5 \cdot 2} - \frac{2 x - 3}{2} \cdot \frac{5}{5} = - 2$

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{(4 x - 3) \cdot 2}{10} - \frac{2 x - 3}{2} \cdot \frac{5}{5} = - 2$

Step 1.3.3

Multiply $\frac{2 x - 3}{2}$ by $\frac{5}{5}$ .

$\frac{(4 x - 3) \cdot 2}{10} - \frac{(2 x - 3) \cdot 5}{2 \cdot 5} = - 2$

Step 1.3.4

Multiply $2$ by $5$ .

$\frac{(4 x - 3) \cdot 2}{10} - \frac{(2 x - 3) \cdot 5}{10} = - 2$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(4 x - 3) \cdot 2 - (2 x - 3) \cdot 5}{10} = - 2$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Apply the distributive property.

$\frac{4 x \cdot 2 - 3 \cdot 2 - (2 x - 3) \cdot 5}{10} = - 2$

Step 1.5.2

Multiply $2$ by $4$ .

$\frac{8 x - 3 \cdot 2 - (2 x - 3) \cdot 5}{10} = - 2$

Step 1.5.3

Multiply $- 3$ by $2$ .

$\frac{8 x - 6 - (2 x - 3) \cdot 5}{10} = - 2$

Step 1.5.4

Apply the distributive property.

$\frac{8 x - 6 + (- (2 x) - - 3) \cdot 5}{10} = - 2$

Step 1.5.5

Multiply $2$ by $- 1$ .

$\frac{8 x - 6 + (- 2 x - - 3) \cdot 5}{10} = - 2$

Step 1.5.6

Multiply $- 1$ by $- 3$ .

$\frac{8 x - 6 + (- 2 x + 3) \cdot 5}{10} = - 2$

Step 1.5.7

Apply the distributive property.

$\frac{8 x - 6 - 2 x \cdot 5 + 3 \cdot 5}{10} = - 2$

Step 1.5.8

Multiply $5$ by $- 2$ .

$\frac{8 x - 6 - 10 x + 3 \cdot 5}{10} = - 2$

Step 1.5.9

Multiply $3$ by $5$ .

$\frac{8 x - 6 - 10 x + 15}{10} = - 2$

Step 1.5.10

Subtract $10 x$ from $8 x$ .

$\frac{- 2 x - 6 + 15}{10} = - 2$

Step 1.5.11

Add $- 6$ and $15$ .

$\frac{- 2 x + 9}{10} = - 2$

Step 1.6

Simplify with factoring out.

Tap for more steps...

Step 1.6.1

Factor $- 1$ out of $- 2 x$ .

$\frac{- (2 x) + 9}{10} = - 2$

Step 1.6.2

Rewrite $9$ as $- 1 (- 9)$ .

$\frac{- (2 x) - 1 (- 9)}{10} = - 2$

Step 1.6.3

Factor $- 1$ out of $- (2 x) - 1 (- 9)$ .

$\frac{- (2 x - 9)}{10} = - 2$

Step 1.6.4

Simplify the expression.

Tap for more steps...

Step 1.6.4.1

Rewrite $- (2 x - 9)$ as $- 1 (2 x - 9)$ .

$\frac{- 1 (2 x - 9)}{10} = - 2$

Step 1.6.4.2

Move the negative in front of the fraction.

$- \frac{2 x - 9}{10} = - 2$

Step 2

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{2 x - 9}{10}) = - 10 \cdot - 2$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $- 10 (- \frac{2 x - 9}{10})$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 3.1.1.1.1

Move the leading negative in $- \frac{2 x - 9}{10}$ into the numerator.

$- 10 \frac{- (2 x - 9)}{10} = - 10 \cdot - 2$

Step 3.1.1.1.2

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- (2 x - 9)}{10} = - 10 \cdot - 2$

Step 3.1.1.1.3

Cancel the common factor.

$10 \cdot - 1 \frac{- (2 x - 9)}{10} = - 10 \cdot - 2$

Step 3.1.1.1.4

Rewrite the expression.

$- - (2 x - 9) = - 10 \cdot - 2$

Step 3.1.1.2

Multiply.

Tap for more steps...

Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (2 x - 9) = - 10 \cdot - 2$

Step 3.1.1.2.2

Multiply $2 x - 9$ by $1$ .

$2 x - 9 = - 10 \cdot - 2$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 10$ by $- 2$ .

$2 x - 9 = 20$

Step 4

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

Tap for more steps...

Step 4.1

Add $9$ to both sides of the equation.

$2 x = 20 + 9$

Step 4.2

Add $20$ and $9$ .

$2 x = 29$

Step 5

Divide each term in $2 x = 29$ by $2$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $2 x = 29$ by $2$ .

$\frac{2 x}{2} = \frac{29}{2}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{29}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{29}{2}$

Step 6

The domain is the set of all valid $x$ values.

${x | x = \frac{29}{2}}$

Step 7