Question

Выяснить какое из чисел -7 -5 0 3 6 является корнем уравнения 71-(11x-14)=20+6(15-x)

Answer 1

71-11x+14=20+90-6x; -11x+6x=20+90-14-71; -5x=25; x=25/(-5)= -5. Ответ: x= -5.

Answer 2

To find out which of the numbers -7, -5, 0, 3, and 6 is a root of the equation 71 - (11x - 14) = 20 + 6(15 - x), we can substitute each of the numbers into the equation and check if it satisfies the equation.

Let's go through each number one by one:

1. -7: Substituting -7 into the equation: 71 - (11(-7) - 14) = 20 + 6(15 - (-7)) 71 - (-77 - 14) = 20 + 6(15 + 7) 71 + 77 + 14 = 20 + 6(22) 162 = 20 + 132 162 = 152

Since 162 is not equal to 152, -7 is not a root of the equation.

2. -5: Substituting -5 into the equation: 71 - (11(-5) - 14) = 20 + 6(15 - (-5)) 71 - (-55 - 14) = 20 + 6(15 + 5) 71 + 55 + 14 = 20 + 6(20) 140 = 20 + 120 140 = 140

Since 140 is equal to 140, -5 is a root of the equation.

3. 0: Substituting 0 into the equation: 71 - (11(0) - 14) = 20 + 6(15 - (0)) 71 - (0 - 14) = 20 + 6(15) 71 - (-14) = 20 + 90 71 + 14 = 20 + 90 85 = 110

Since 85 is not equal to 110, 0 is not a root of the equation.

4. 3: Substituting 3 into the equation: 71 - (11(3) - 14) = 20 + 6(15 - 3) 71 - (33 - 14) = 20 + 6(12) 71 - 19 = 20 + 72 52 = 92

Since 52 is not equal to 92, 3 is not a root of the equation.

5. 6: Substituting 6 into the equation: 71 - (11(6) - 14) = 20 + 6(15 - 6) 71 - (66 - 14) = 20 + 6(9) 71 - 52 = 20 + 54 19 = 74

Since 19 is not equal to 74, 6 is not a root of the equation.

Therefore, the only number that is a root of the equation is -5.