Solve for x 2(1-5/2x)+5x=2

$2 (1 - \frac{5}{2} x) + 5 x = 2$

Step 1

Simplify $2 (1 - \frac{5}{2} x) + 5 x$ .

Simplify each term.

Combine $x$ and $\frac{5}{2}$ .

$2 (1 - \frac{x \cdot 5}{2}) + 5 x = 2$

Move $5$ to the left of $x$ .

$2 (1 - \frac{5 x}{2}) + 5 x = 2$

Apply the distributive property.

$2 \cdot 1 + 2 (- \frac{5 x}{2}) + 5 x = 2$

Multiply $2$ by $1$ .

$2 + 2 (- \frac{5 x}{2}) + 5 x = 2$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$2 + 2 \frac{- 5 x}{2} + 5 x = 2$

Cancel the common factor.

$2 + 2 \frac{- 5 x}{2} + 5 x = 2$

Rewrite the expression.

$2 - 5 x + 5 x = 2$

Combine the opposite terms in $2 - 5 x + 5 x$ .

Add $- 5 x$ and $5 x$ .

$2 + 0 = 2$

Add $2$ and $0$ .

$2 = 2$

Step 2

Since $2 = 2$ , the equation will always be true for any value of $x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$