Question

|4 + x| < 7 пжпжпжпжпжпж

Answer 1

Відповідь:

х=1 або 2

4+1=5

4+2=6

І4+хІ < 7

5 < 7

6 < 7

Answer 2

To solve the absolute value inequality |4 + x| < 7, you can break it down into two separate cases:

Case 1: 4 + x is positive (i.e., 4 + x > 0) In this case, the inequality becomes:

4 + x < 7

Now, solve for x:

x < 7 - 4 x < 3

So, in this case, the solution is x < 3.

Case 2: 4 + x is negative (i.e., 4 + x < 0) In this case, you need to negate the absolute value to make it positive:

-(4 + x) < 7

Now, solve for x:

-4 - x < 7

To isolate x, first add 4 to both sides:

-x < 7 + 4 -x < 11

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

x > -11

So, in this case, the solution is x > -11.

Now, combine the solutions from both cases:

x < 3 (from Case 1) x > -11 (from Case 2)

The final solution is the intersection of these two cases:

-11 < x < 3

So, the solution to the inequality |4 + x| < 7 is -11 < x < 3.