Solve the Inequality for x (4x-3)/2>=-3.5

$\frac{4 x - 3}{2} \geq - 3.5$

Step 1

Multiply both sides by $2$ .

$\frac{4 x - 3}{2} \cdot 2 \geq - 3.5 \cdot 2$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 x - 3}{2} \cdot 2 \geq - 3.5 \cdot 2$

Rewrite the expression.

$4 x - 3 \geq - 3.5 \cdot 2$

Simplify the right side.

Multiply $- 3.5$ by $2$ .

$4 x - 3 \geq - 7$

Step 3

Solve for $x$ .

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

Add $3$ to both sides of the inequality.

$4 x \geq - 7 + 3$

Add $- 7$ and $3$ .

$4 x \geq - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $4$ .

$x \geq - 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 1$

Interval Notation:

$[- 1, \infty)$