Solve the Inequality for x 100+55x>150+51x

$100 + 55 x > 150 + 51 x$

Step 1

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

Subtract $51 x$ from both sides of the inequality.

$100 + 55 x - 51 x > 150$

Subtract $51 x$ from $55 x$ .

$100 + 4 x > 150$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

Subtract $100$ from both sides of the inequality.

$4 x > 150 - 100$

Subtract $100$ from $150$ .

$4 x > 50$

Step 3

Divide each term in $4 x > 50$ by $4$ and simplify.

Divide each term in $4 x > 50$ by $4$ .

$\frac{4 x}{4} > \frac{50}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{50}{4}$

Divide $x$ by $1$ .

$x > \frac{50}{4}$

Simplify the right side.

Cancel the common factor of $50$ and $4$ .

Factor $2$ out of $50$ .

$x > \frac{2 (25)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x > \frac{2 \cdot 25}{2 \cdot 2}$

Cancel the common factor.

$x > \frac{2 \cdot 25}{2 \cdot 2}$

Rewrite the expression.

$x > \frac{25}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{25}{2}$

Interval Notation:

$(\frac{25}{2}, \infty)$