To solve this inequality, we first need to simplify the expression on the left side:
x3+8x2+50x2+x−7x³ + 8x² + 50x² + x - 7x3+8x2+50x2+x−7 / x−7x - 7x−7
Combine like terms in the numerator:
x3+58x2+x−7x³ + 58x² + x - 7x3+58x2+x−7 / x−7x - 7x−7
Now we can divide the numerator by the denominator using long division or synthetic division:
x² + 7x + 1 + 0
Now our inequality becomes:
x² + 7x + 1 ≤ 1
Next, we subtract 1 from both sides:
x² + 7x ≤ 0
Now we have a quadratic inequality that we can solve by factoring or using the quadratic formula. The solutions are x = 0 and x = -7.
Therefore, the solution to the original inequality is -7 ≤ x ≤ 0.
To solve this inequality, we first need to simplify the expression on the left side:
x3+8x2+50x2+x−7x³ + 8x² + 50x² + x - 7x3+8x2+50x2+x−7 / x−7x - 7x−7
Combine like terms in the numerator:
x3+58x2+x−7x³ + 58x² + x - 7x3+58x2+x−7 / x−7x - 7x−7
Now we can divide the numerator by the denominator using long division or synthetic division:
x² + 7x + 1 + 0
Now our inequality becomes:
x² + 7x + 1 ≤ 1
Next, we subtract 1 from both sides:
x² + 7x ≤ 0
Now we have a quadratic inequality that we can solve by factoring or using the quadratic formula. The solutions are x = 0 and x = -7.
Therefore, the solution to the original inequality is -7 ≤ x ≤ 0.