Question

А)|x|=-5,2 б)|x+15|=2 в)|7x-8|=8 г)(7x+5)(4x-13)=0 д)x(x-20)(x-21)(x+20)(x+21)=0

Answer 1

Ответ:

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Answer 2

a) |x| = -5

The equation |x| = -5 represents the absolute value of x equal to -5. However, the absolute value of any real number is always non-negative. Therefore, there are no solutions to this equation. In other words, there is no real number x that satisfies the equation |x| = -5.

б) |x + 15| = 2

The equation |x + 15| = 2 represents the absolute value of (x + 15) equal to 2. To solve this equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: x + 15 > 0 If x + 15 > 0, then the equation simplifies to x + 15 = 2. Solving this equation gives us x = -13.

Case 2: x + 15 < 0 If x + 15 < 0, then the equation simplifies to -(x + 15) = 2. Solving this equation gives us x = -17.

Therefore, the solutions to the equation |x + 15| = 2 are x = -13 and x = -17.

в) |7x - 8| = 8

The equation |7x - 8| = 8 represents the absolute value of (7x - 8) equal to 8. Similar to the previous equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 7x - 8 > 0 If 7x - 8 > 0, then the equation simplifies to 7x - 8 = 8. Solving this equation gives us x = 2.

Case 2: 7x - 8 < 0 If 7x - 8 < 0, then the equation simplifies to -(7x - 8) = 8. Solving this equation gives us x = 16/7.

Therefore, the solutions to the equation |7x - 8| = 8 are x = 2 and x = 16/7.

г) (7x + 5)(4x - 13) = 0

The equation (7x + 5)(4x - 13) = 0 represents the product of two expressions equal to zero. To find the solutions, we set each expression equal to zero and solve for x.

Setting 7x + 5 = 0, we get x = -5/7. Setting 4x - 13 = 0, we get x = 13/4.

Therefore, the solutions to the equation (7x + 5)(4x - 13) = 0 are x = -5/7 and x = 13/4.

д) x(x - 20)(x - 21)(x + 20)(x + 21) = 0

The equation x(x - 20)(x - 21)(x + 20)(x + 21) = 0 represents the product of five expressions equal to zero. To find the solutions, we set each expression equal to zero and solve for x.

Setting x = 0, we get one solution x = 0. Setting x - 20 = 0, we get x = 20. Setting x - 21 = 0, we get x = 21. Setting x + 20 = 0, we get x = -20. Setting x + 21 = 0, we get x = -21.

Therefore, the solutions to the equation x(x - 20)(x - 21)(x + 20)(x + 21) = 0 are x = 0, x = 20, x = 21, x = -20, and x = -21.