Algebra Examples

$- 3 (10 - x) = 11 x - 2 (4 x + 15)$

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.

$11 x - 2 (4 x + 15) = - 3 (10 - x)$

Step 2

Simplify $11 x - 2 (4 x + 15)$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$11 x - 2 (4 x) - 2 \cdot 15 = - 3 (10 - x)$

Step 2.1.2

Multiply $4$ by $- 2$ .

$11 x - 8 x - 2 \cdot 15 = - 3 (10 - x)$

Step 2.1.3

Multiply $- 2$ by $15$ .

$11 x - 8 x - 30 = - 3 (10 - x)$

Step 2.2

Subtract $8 x$ from $11 x$ .

$3 x - 30 = - 3 (10 - x)$

Step 3

Simplify $- 3 (10 - x)$ .

Tap for more steps...

Step 3.1

Apply the distributive property.

$3 x - 30 = - 3 \cdot 10 - 3 (- x)$

Step 3.2

Multiply.

Tap for more steps...

Step 3.2.1

Multiply $- 3$ by $10$ .

$3 x - 30 = - 30 - 3 (- x)$

Step 3.2.2

Multiply $- 1$ by $- 3$ .

$3 x - 30 = - 30 + 3 x$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $3 x$ from both sides of the equation.

$3 x - 30 - 3 x = - 30$

Step 4.2

Combine the opposite terms in $3 x - 30 - 3 x$ .

Tap for more steps...

Step 4.2.1

Subtract $3 x$ from $3 x$ .

$0 - 30 = - 30$

Step 4.2.2

Subtract $30$ from $0$ .

$- 30 = - 30$

Step 5

Since $- 30 = - 30$ , the equation will always be true for any value of $x$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$