Solve the System of Inequalities 0.4x-1<=0 2.3x>=4.6

$0.4 x - 1 \leq 0$ $2.3 x \geq 4.6$

Solve $0.4 x - 1 \leq 0$ for $x$ .

Add $1$ to both sides of the inequality.

$0.4 x \leq 1$

Divide each term in $0.4 x \leq 1$ by $0.4$ and simplify.

Divide each term in $0.4 x \leq 1$ by $0.4$ .

$\frac{0.4 x}{0.4} \leq \frac{1}{0.4}$

Simplify the left side.

Cancel the common factor of $0.4$ .

Cancel the common factor.

$\frac{0.4 x}{0.4} \leq \frac{1}{0.4}$

Divide $x$ by $1$ .

$x \leq \frac{1}{0.4}$

Simplify the right side.

Divide $1$ by $0.4$ .

$x \leq 2.5$

Divide each term in $2.3 x \geq 4.6$ by $2.3$ and simplify.

Divide each term in $2.3 x \geq 4.6$ by $2.3$ .

$\frac{2.3 x}{2.3} \geq \frac{4.6}{2.3}$

Simplify the left side.

Cancel the common factor of $2.3$ .

Cancel the common factor.

$\frac{2.3 x}{2.3} \geq \frac{4.6}{2.3}$

Divide $x$ by $1$ .

$x \geq \frac{4.6}{2.3}$

Simplify the right side.

Divide $4.6$ by $2.3$ .

$x \geq 2$

Find the intersection of $x \leq 2.5$ and $x \geq 2$ .

$2 \leq x \leq 2.5$

The result can be shown in multiple forms.

Inequality Form:

$2 \leq x \leq 2.5$

Interval Notation:

$[2, 2.5]$