Solve the Inequality for x 1/2(8x+1)>=3x+5/2

$\frac{1}{2} (8 x + 1) \geq 3 x + \frac{5}{2}$

Simplify $\frac{1}{2} \cdot (8 x + 1)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (8 x + 1) \geq 3 x + \frac{5}{2}$

Simplify by adding zeros.

$\frac{1}{2} \cdot (8 x + 1) \geq 3 x + \frac{5}{2}$

Apply the distributive property.

$\frac{1}{2} (8 x) + \frac{1}{2} \cdot 1 \geq 3 x + \frac{5}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $8 x$ .

$\frac{1}{2} (2 (4 x)) + \frac{1}{2} \cdot 1 \geq 3 x + \frac{5}{2}$

Cancel the common factor.

$\frac{1}{2} (2 (4 x)) + \frac{1}{2} \cdot 1 \geq 3 x + \frac{5}{2}$

Rewrite the expression.

$4 x + \frac{1}{2} \cdot 1 \geq 3 x + \frac{5}{2}$

Multiply $\frac{1}{2}$ by $1$ .

$4 x + \frac{1}{2} \geq 3 x + \frac{5}{2}$

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

Subtract $3 x$ from both sides of the inequality.

$4 x + \frac{1}{2} - 3 x \geq \frac{5}{2}$

Subtract $3 x$ from $4 x$ .

$x + \frac{1}{2} \geq \frac{5}{2}$

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

Subtract $\frac{1}{2}$ from both sides of the inequality.

$x \geq \frac{5}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$x \geq \frac{5 - 1}{2}$

Subtract $1$ from $5$ .

$x \geq \frac{4}{2}$

Divide $4$ by $2$ .

$x \geq 2$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$