Solve the Inequality for x 5x+7<=8x-3+2x

$5 x + 7 \leq 8 x - 3 + 2 x$

Rewrite so $x$ is on the left side of the inequality.

$8 x - 3 + 2 x \geq 5 x + 7$

Add $8 x$ and $2 x$ .

$10 x - 3 \geq 5 x + 7$

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

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

$10 x - 3 - 5 x \geq 7$

Subtract $5 x$ from $10 x$ .

$5 x - 3 \geq 7$

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

Add $3$ to both sides of the inequality.

$5 x \geq 7 + 3$

Add $7$ and $3$ .

$5 x \geq 10$

Divide each term in $5 x \geq 10$ by $5$ and simplify.

Divide each term in $5 x \geq 10$ by $5$ .

$\frac{5 x}{5} \geq \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{10}{5}$

Divide $x$ by $1$ .

$x \geq \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$x \geq 2$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$