Finite Math Examples

$2 (x - 8) + 7 = 5 (x + 2) - 3 x - 19$

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.

$5 (x + 2) - 3 x - 19 = 2 (x - 8) + 7$

Step 2

Simplify $5 (x + 2) - 3 x - 19$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$5 x + 5 \cdot 2 - 3 x - 19 = 2 (x - 8) + 7$

Step 2.1.2

Multiply $5$ by $2$ .

$5 x + 10 - 3 x - 19 = 2 (x - 8) + 7$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Subtract $3 x$ from $5 x$ .

$2 x + 10 - 19 = 2 (x - 8) + 7$

Step 2.2.2

Subtract $19$ from $10$ .

$2 x - 9 = 2 (x - 8) + 7$

Step 3

Simplify $2 (x - 8) + 7$ .

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Apply the distributive property.

$2 x - 9 = 2 x + 2 \cdot - 8 + 7$

Step 3.1.2

Multiply $2$ by $- 8$ .

$2 x - 9 = 2 x - 16 + 7$

Step 3.2

Add $- 16$ and $7$ .

$2 x - 9 = 2 x - 9$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $2 x$ from both sides of the equation.

$2 x - 9 - 2 x = - 9$

Step 4.2

Combine the opposite terms in $2 x - 9 - 2 x$ .

Tap for more steps...

Step 4.2.1

Subtract $2 x$ from $2 x$ .

$0 - 9 = - 9$

Step 4.2.2

Subtract $9$ from $0$ .

$- 9 = - 9$

Step 5

Since $- 9 = - 9$ , 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:

$(- \infty, \infty)$