Question

|х+3|<7 ........................................................................

Answer 1

Ответ:

х=3,-3,2,-2,1,-1,0 и бесконечное множество отрицательных чисел

Answer 2

The inequality you've provided is:

|х + 3| < 7

To solve this inequality, we can break it down into two cases, one for when the expression inside the absolute value is positive and one for when it's negative.

Case 1: x + 3 is positive: In this case, the absolute value is not needed, so we have:

x + 3 < 7

Now, we can solve for x:

x < 7 - 3 x < 4

Case 2: x + 3 is negative: In this case, we need to consider the negative value inside the absolute value. When the expression inside the absolute value is negative, we need to negate it to make it positive:

-(x + 3) < 7

Now, we can solve for x:

-x - 3 < 7

Add 3 to both sides:

-x < 7 + 3 -x < 10

Now, multiply both sides by -1 (remember to reverse the inequality when multiplying by a negative number):

x > -10

So, the two cases give us the following solutions:

Case 1: x < 4 Case 2: x > -10

To find the combined solution, we take the intersection of these two cases:

-10 < x < 4

So, the solution to the inequality |х + 3| < 7 is -10 < x < 4, which means that x can take any value between -10 (exclusive) and 4 (exclusive) for the inequality to hold true.