The solution of the given inequality y ≤ -x² + 2x is (x,y) ≥ {(0,0) and (-2,-4)} obtained by plotting graph between axis.
A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Given the inequality,
y ≤ −x² + 2x
The inequality consists of two functions,
y ≤ -x² and y ≤ 2x
Now if we plot both inequalities
x = 0 ⇒ y = 0
And,
2x ≤ -x²
-x²/x ≥ 2
x ≤ -2
So,
y ≤ 2(-2)
y ≤ -4
If we plot both as shown below then the bounded region is obtained towards the right therefore the solution will be greater than this.
Therefore (x,y) ≥ {(0,0) and (-2,-4)} will be solution.
Hence "The solution of the given inequality y ≤ -x² + 2x is (x,y) ≥ {(0,0) and (-2,-4)} obtained by plotting graph between axis".
For more about inequality,
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