Solve the Inequality for x 4x+1+2x>=5

$4 x + 1 + 2 x \geq 5$

Add $4 x$ and $2 x$ .

$6 x + 1 \geq 5$

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

Subtract $1$ from both sides of the inequality.

$6 x \geq 5 - 1$

Subtract $1$ from $5$ .

$6 x \geq 4$

Divide each term in $6 x \geq 4$ by $6$ and simplify.

Divide each term in $6 x \geq 4$ by $6$ .

$\frac{6 x}{6} \geq \frac{4}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} \geq \frac{4}{6}$

Divide $x$ by $1$ .

$x \geq \frac{4}{6}$

Simplify the right side.

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$x \geq \frac{2 (2)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x \geq \frac{2 \cdot 2}{2 \cdot 3}$

Cancel the common factor.

$x \geq \frac{2 \cdot 2}{2 \cdot 3}$

Rewrite the expression.

$x \geq \frac{2}{3}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{2}{3}$

Interval Notation:

$[\frac{2}{3}, \infty)$