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# \sqrt(x^(2)-13x+12)<=5-x

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\sqrt(x^(2)-13x+12)<=5-x

Dec 24, 2019

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Hints:

-Square both sides

-Solve the equation for x

-Remember when dividing by - or multiplying by - we multiply both sides and in inequalities, we switch the sign e.g, if it is < then it will be > if being multiplied or divided by -)

-If real numbers find intervals

Dec 24, 2019
#2
+106516
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√ [x^2 - 13x + 12]  ≤  5 - x   square both sides

x^2  - 13x + 12  ≤   x^2  - 10x  +  25       simplify

-3x ≤ 13       divide both sides by   -3, reverse the inequality sign

x ≥ - 13/3

But   we also   must have that

x^2 - 13x + 12  ≥ 0

(x - 12) ( x - 1) ≥ 0

The solutions to this are

(-inf, 1 ]  U  [12, inf)

We must take the  most restrictive interval....this is

-13/3 ≤ x ≤ 1

Dec 24, 2019