Algebra Examples

$b (5 p x - 3 c) = a (q x - 4)$

Step 1

Simplify $b (5 p x - 3 c)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + b (5 p x - 3 c) = a (q x - 4)$

Step 1.2

Simplify by adding zeros.

$b (5 p x - 3 c) = a (q x - 4)$

Step 1.3

Apply the distributive property.

$b (5 p x) + b (- 3 c) = a (q x - 4)$

Step 1.4

Reorder.

Tap for more steps...

Step 1.4.1

Rewrite using the commutative property of multiplication.

$5 b p x + b (- 3 c) = a (q x - 4)$

Step 1.4.2

Rewrite using the commutative property of multiplication.

$5 b p x - 3 b c = a (q x - 4)$

Step 2

Simplify $a (q x - 4)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$5 b p x - 3 b c = a (q x) + a \cdot - 4$

Step 2.2

Move $- 4$ to the left of $a$ .

$5 b p x - 3 b c = a q x - 4 a$

Step 3

Subtract $a q x$ from both sides of the equation.

$5 b p x - 3 b c - a q x = - 4 a$

Step 4

Add $3 b c$ to both sides of the equation.

$5 b p x - a q x = - 4 a + 3 b c$

Step 5

Factor $x$ out of $5 b p x - a q x$ .

Tap for more steps...

Step 5.1

Factor $x$ out of $5 b p x$ .

$x (5 b p) - a q x = - 4 a + 3 b c$

Step 5.2

Factor $x$ out of $- a q x$ .

$x (5 b p) + x (- a q) = - 4 a + 3 b c$

Step 5.3

Factor $x$ out of $x (5 b p) + x (- a q)$ .

$x (5 b p - a q) = - 4 a + 3 b c$

Step 6

Divide each term in $x (5 b p - a q) = - 4 a + 3 b c$ by $5 b p - a q$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $x (5 b p - a q) = - 4 a + 3 b c$ by $5 b p - a q$ .

$\frac{x (5 b p - a q)}{5 b p - a q} = \frac{- 4 a}{5 b p - a q} + \frac{3 b c}{5 b p - a q}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $5 b p - a q$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{x (5 b p - a q)}{5 b p - a q} = \frac{- 4 a}{5 b p - a q} + \frac{3 b c}{5 b p - a q}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4 a}{5 b p - a q} + \frac{3 b c}{5 b p - a q}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Combine the numerators over the common denominator.

$x = \frac{- 4 a + 3 b c}{5 b p - a q}$

Step 6.3.2

Factor $- 1$ out of $- 4 a$ .

$x = \frac{- (4 a) + 3 b c}{5 b p - a q}$

Step 6.3.3

Factor $- 1$ out of $3 b c$ .

$x = \frac{- (4 a) - (- 3 b c)}{5 b p - a q}$

Step 6.3.4

Factor $- 1$ out of $- (4 a) - (- 3 b c)$ .

$x = \frac{- (4 a - 3 b c)}{5 b p - a q}$

Step 6.3.5

Simplify the expression.

Tap for more steps...

Step 6.3.5.1

Rewrite $- (4 a - 3 b c)$ as $- 1 (4 a - 3 b c)$ .

$x = \frac{- 1 (4 a - 3 b c)}{5 b p - a q}$

Step 6.3.5.2

Move the negative in front of the fraction.

$x = - \frac{4 a - 3 b c}{5 b p - a q}$