Add 2x and subtract 7
5 -2x +2x < 7 +2x . . . . . . showing 2x added
5 < 7 +2x . . . . . . . . . . . .. simplified
5 -7 < 7 -7 +2x . . . . . . . . showing 7 subtracted
-2 < 2x . . . . . . . . . . . . . . . simplified
Now, divide by 2
-1 < x
The solution is -1 < x.
I would say 2.5 because that would be exactly in the middle
Answer:
Step-by-step explanation:
- 10x² - 7ax + (a + 2) (a - 5) =
- 10x² - 7ax + a² - 3a - 10
Factorize by finding the roots
<u>Find the discriminant:</u>
- D = b² - 4ac
- D = (-7a)² - 4*10*(a² - 3a - 10) =
- 49a² - 40a² + 120a + 400 =
- 9a² + 120a + 400 =
- (3a + 20)²
<u>Find the roots:</u>
- x = (- b ± √D)/2a = (7a ± (3a + 20)) / 20
- x₁ = (7a + 3a + 20) / 20 = (10a + 20) / 20 = (a + 2) / 2
- x₂ = (7a - 3a - 20) / 20 = (4a - 20) / 20 = (a - 5) / 5
<u>Factorize the expression:</u>
- 10x² - 7ax + a² - 3a - 10 =
- 10 (x - x₁)(x - x₂) =
- 10[x - (a + 2)/2][[x - (a - 5)/5] =
- (2x - a - 2)(5x - a + 5)
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<u>You would also try a shorter but more difficult way:</u>
- 10x² - 7ax + (a + 2) (a - 5) =
- 2x*5x - 2ax + 10x - 5ax - 10x + (a + 2) (a - 5) =
- 2x*5x - 2x(a - 5) - 5x(a + 2) + (a + 2) (a - 5) =
- 2x(5x - (a - 5)) - (a + 2)(5x - (a - 5)) =
- (5x - a + 5)(2x - a - 2)
