Question

solve the inequality group: \

$$\begin{cases} 5(x - 6500) - 30000 < 2x + 52700 \\\\ 6x < 5x + 7200 \\end{cases}$$

Explanation:

Step 1: Simplify left side

$5(x - 6500)-30000 = 5x - 32500 - 30000 = 5x - 62500$

Step 2: Rewrite inequality

Now the inequality is $5x - 62500 < 2x + 52700$

Step 3: Subtract 2x from both sides

$5x - 2x - 62500 < 52700$ which simplifies to $3x - 62500 < 52700$

Step 4: Add 62500 to both sides

$3x < 52700 + 62500$ so $3x < 115200$

Step 5: Divide by 3

$x < \frac{115200}{3}$ which gives $x < 38400$

Answer:

$x < 38400$