Precalculus Examples

$3 (2 x - 1) = 7 x - (3 - 5 x) + (- x + 24)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$7 x - (3 - 5 x) - x + 24 = 3 (2 x - 1)$

Step 2

Simplify $7 x - (3 - 5 x) - x + 24$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$7 x - 1 \cdot 3 - (- 5 x) - x + 24 = 3 (2 x - 1)$

Step 2.1.2

Multiply $- 1$ by $3$ .

$7 x - 3 - (- 5 x) - x + 24 = 3 (2 x - 1)$

Step 2.1.3

Multiply $- 5$ by $- 1$ .

$7 x - 3 + 5 x - x + 24 = 3 (2 x - 1)$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Add $7 x$ and $5 x$ .

$12 x - 3 - x + 24 = 3 (2 x - 1)$

Step 2.2.2

Subtract $x$ from $12 x$ .

$11 x - 3 + 24 = 3 (2 x - 1)$

Step 2.2.3

Add $- 3$ and $24$ .

$11 x + 21 = 3 (2 x - 1)$

Step 3

Simplify $3 (2 x - 1)$ .

Tap for more steps...

Step 3.1

Apply the distributive property.

$11 x + 21 = 3 (2 x) + 3 \cdot - 1$

Step 3.2

Multiply.

Tap for more steps...

Step 3.2.1

Multiply $2$ by $3$ .

$11 x + 21 = 6 x + 3 \cdot - 1$

Step 3.2.2

Multiply $3$ by $- 1$ .

$11 x + 21 = 6 x - 3$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $6 x$ from both sides of the equation.

$11 x + 21 - 6 x = - 3$

Step 4.2

Subtract $6 x$ from $11 x$ .

$5 x + 21 = - 3$

Step 5

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

Tap for more steps...

Step 5.1

Subtract $21$ from both sides of the equation.

$5 x = - 3 - 21$

Step 5.2

Subtract $21$ from $- 3$ .

$5 x = - 24$

Step 6

Divide each term in $5 x = - 24$ by $5$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $5 x = - 24$ by $5$ .

$\frac{5 x}{5} = \frac{- 24}{5}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 24}{5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 24}{5}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Move the negative in front of the fraction.

$x = - \frac{24}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{24}{5}$

Decimal Form:

$x = - 4.8$

Mixed Number Form:

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