rational inequalities General mathematics 11 new.pptx

grade 11 general mathematics

1. T N I O A A L R L Q E N A U E S I I T I Gen- Math Teacher: Jezra Mae L. Galacyan STEM- A Good Morning!

2. T N I O A A L R L Q E N A U E S I I T I

3. RATIONAL INEQUALITIES A rational inequality is an inequality involving a rational expression, which is a fraction where the numerator and denominator are polynomials. 3

4. RATIONAL INEQUALITIES General form f(x)/g(x) < 0, f(x)/g(x) > 0, f(x)/g(x) ≤ 0, or f(x)/g(x) ≥ 0 EXAMPLES 4

5. 5 Let’s solve : LCD: 6 , 12, 18 3, 6 , 9 [ [ 6 18x -5 ≥4x 18x+4x ≥ 5 22x ≥ 5 22x ≥ 5 22 22 x ≥ 5 22 or 5 22 8 , 1 5 22 8

6. 6

7. 7 INTERVAL (-∞, 2) (2, 4) (4, ∞) Test Point 1 3 5 -2x+8 6 2 -2 x-2 -1 1 3 -2x+8 ── x-2 - + -

8. 8 >0 >0 >0 >0   x²-x=0 x(x-1)=0 x=0 x=1 x+3=0 x= -3 x-3=0 x=3

9. 9 x²-x=0 x(x-1)=0 x=0 x=1 x+3=0 x= -3 x-3=0 x=3 Interval (-∞, -3) (-3, 0) (0, 1) (1, 3) (3, ∞) Test Point -4 -1 0.5 2 4 x²-x 20 2 -0.25 2 12 ) 7 -8 -8.75 -5 7 + - + - + Interval (-∞, -3) (-3, 0) (0, 1) (1, 3) (3, ∞) Test Point -4 -1 0.5 2 4 x²-x 20 2 -0.25 2 12 7 -8 -8.75 -5 7 + - + - +

10. Exercise more 10

11. 11 -10x-24=0 x =   2x+5=0 x =       x<   < x <   x >   INTERVAL (-∞, ) ( , ) ( , ∞) Test Point -3 -2.45 -1 -10x-24 6 0.5 -14 2x+5 -1 0.1 3 - + - INTERVAL Test Point -3 -2.45 -1 -10x-24 6 0.5 -14 2x+5 -1 0.1 3 - + -

12. 12   [ -2x-2=0 x=-1   Solve for x

13. 13 10+5(x-5)-2(x+3)≤0 10+5x-25-2x-6≤0 3x-21≤0 x≤7