Question

Решите уравнение |х-3|=7

Answer 1

X-3=7; x=7+3; x=10
x-3=-7; x=-7+3; x=-4
x1=-4; x2=10

Answer 2

$|x-3|=7 \\1) \left \{ {{x-3\geq 0 } \atop {x-3=7}} \right. ; \left \{ {{x\geq 3} \atop {x=10}} \right. \\2) \left \{ {{x-3< 0 } \atop {-x+3=7}} \right. ; \left \{ {{x$

Ответ : x=10;-4

Answer 3

To solve the absolute value equation |x - 3| = 7, we need to consider both the positive and negative cases.

1. Positive case: When x - 3 is positive (x - 3 > 0), the equation becomes: x - 3 = 7

Add 3 to both sides: x = 7 + 3 x = 10

2. Negative case: When x - 3 is negative (x - 3 < 0), we must take the absolute value of the negative quantity: |x - 3| = -(x - 3)

So the equation becomes: -(x - 3) = 7

Multiply both sides by -1 to get rid of the negative sign: x - 3 = -7

Add 3 to both sides: x = -7 + 3 x = -4

Thus, the solutions to the absolute value equation are x = 10 and x = -4.