Solve for x 5(x+2)+4=8x-1-3(x-5)

$5 (x + 2) + 4 = 8 x - 1 - 3 (x - 5)$

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.

$8 x - 1 - 3 (x - 5) = 5 (x + 2) + 4$

Step 2

Simplify $8 x - 1 - 3 (x - 5)$ .

Simplify each term.

Apply the distributive property.

$8 x - 1 - 3 x - 3 \cdot - 5 = 5 (x + 2) + 4$

Multiply $- 3$ by $- 5$ .

$8 x - 1 - 3 x + 15 = 5 (x + 2) + 4$

Simplify by adding terms.

Subtract $3 x$ from $8 x$ .

$5 x - 1 + 15 = 5 (x + 2) + 4$

Add $- 1$ and $15$ .

$5 x + 14 = 5 (x + 2) + 4$

Step 3

Simplify $5 (x + 2) + 4$ .

Simplify each term.

Apply the distributive property.

$5 x + 14 = 5 x + 5 \cdot 2 + 4$

Multiply $5$ by $2$ .

$5 x + 14 = 5 x + 10 + 4$

Add $10$ and $4$ .

$5 x + 14 = 5 x + 14$

Step 4

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

Subtract $5 x$ from both sides of the equation.

$5 x + 14 - 5 x = 14$

Combine the opposite terms in $5 x + 14 - 5 x$ .

Subtract $5 x$ from $5 x$ .

$0 + 14 = 14$

Add $0$ and $14$ .

$14 = 14$

Step 5

Since $14 = 14$ , 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:

$(- \infty, \infty)$