Question

solve for x
\

$$\begin{cases} y \\geq 2x - 1 y < -x + 4 \\end{cases}$$

Explanation:

Step1: Set inequalities equal

$2x - 1 = -x + 4$

Step2: Isolate x terms

$2x + x = 4 + 1$

Step3: Simplify and solve for x

$3x = 5$
$x = \frac{5}{3}$

Step4: Analyze inequality range

Since $2x-1 < y < -x+4$, we need $2x-1 < -x+4$, which simplifies to $x < \frac{5}{3}$.

Answer:

$x < \frac{5}{3}$