How many different integer values of x satisfy |𝑥+6|<3?

To solve the inequality |x+6|<3, we can break it down into two separate inequalities because of the absolute value.

1. The first inequality is x + 6 < 3.
2. The second inequality is -(x + 6) < 3.

Solving these two inequalities will give us the range of x values that satisfy the original inequality.

1. For the first inequality, subtract 6 from both sides to isolate x:

   x + 6 - 6 < 3 - 6 x < -3

2. For the second inequality, distribute the negative sign and then add 6 to both sides:

   -x - 6 < 3 -x < 3 + 6 -x < 9

   To solve for x, we need to multiply or divide by -1, but remember that this flips the inequality sign:

   x > -9

So, the solution to the original inequality |x+6|<3 is -9 < x < -3.

The integer values of x that satisfy this inequality are -8, -7, -6, -5, and -4. So, there are 5 different integer values of x that satisfy |x+6|<3.