Let's first expand the terms on both sides of the inequality:
(x-3)² = x² - 6x + (5+x)² = x² + 10x + 25
Now, our inequality becomes:
x² - 6x + 9 ≤ x² + 10x + 25
Subtract x² from both sides to simplify:
-6x + 9 ≤ 10x + 25
Subtract 10x from both sides:
-16x + 9 ≤ 25
Subtract 9 from both sides:
-16x ≤ 16
Divide by -16 (Note: when dividing by a negative number, the direction of the inequality changes):
x ≥ -1
Therefore, the solution to the inequality (x-3)² ≤ (5+x)² is x ≥ -1.
Let's first expand the terms on both sides of the inequality:
(x-3)² = x² - 6x +
(5+x)² = x² + 10x + 25
Now, our inequality becomes:
x² - 6x + 9 ≤ x² + 10x + 25
Subtract x² from both sides to simplify:
-6x + 9 ≤ 10x + 25
Subtract 10x from both sides:
-16x + 9 ≤ 25
Subtract 9 from both sides:
-16x ≤ 16
Divide by -16 (Note: when dividing by a negative number, the direction of the inequality changes):
x ≥ -1
Therefore, the solution to the inequality (x-3)² ≤ (5+x)² is x ≥ -1.