Algebra Examples

$3 (x + 5) = 5 (x + 3) - 2 x$

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.

$5 (x + 3) - 2 x = 3 (x + 5)$

Step 2

Simplify $5 (x + 3) - 2 x$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $5$ by $3$ .

$5 x + 15 - 2 x = 3 (x + 5)$

Step 2.2

Subtract $2 x$ from $5 x$ .

$3 x + 15 = 3 (x + 5)$

Step 3

Simplify $3 (x + 5)$ .

Tap for more steps...

Step 3.1

Apply the distributive property.

$3 x + 15 = 3 x + 3 \cdot 5$

Step 3.2

Multiply $3$ by $5$ .

$3 x + 15 = 3 x + 15$

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.

$3 x + 15 - 3 x = 15$

Step 4.2

Combine the opposite terms in $3 x + 15 - 3 x$ .

Tap for more steps...

Step 4.2.1

Subtract $3 x$ from $3 x$ .

$0 + 15 = 15$

Step 4.2.2

Add $0$ and $15$ .

$15 = 15$

Step 5

Since $15 = 15$ , 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:

$(- \infty, \infty)$