How many different integer values of x satisfy |𝑥+5|<4?

To solve the inequality |x+5|<4, we can break it down into two separate inequalities because of the absolute value.

1. The first inequality is x + 5 < 4.
2. The second inequality is -(x + 5) < 4.

Now, we can solve each inequality separately:

1. For the first inequality, subtract 5 from both sides to isolate x: x < 4 - 5, which simplifies to x < -1.
2. For the second inequality, distribute the negative sign: -x - 5 < 4. Then, add 5 to both sides to isolate -x: -x < 4 + 5, which simplifies to -x < 9. Multiply both sides by -1 to solve for x, remembering to flip the inequality sign: x > -9.

So, the solution to the inequality |x+5|<4 is -9 < x < -1.

The integer values of x that satisfy this inequality are -8, -7, -6, -5, -4, -3, -2. So, there are 7 different integer values of x that satisfy the inequality.

To solve the inequality |x+5|<4, we need to consider two cases because of the absolute value.

Case 1: x + 5 < 4 Subtract 5 from both sides to isolate x: x < 4 - 5, which simplifies to x < -1.

Case 2: -(x + 5) < 4 Distribute the negative sign: -x - 5 < 4. Add 5 to both sides to isolate x: -x < 4 + 5, which simplifies to -x < 9. Multiply both sides by -1 to solve for x. Remember to flip the inequality sign when multiplying by a negative number: x > -9.

So the solution to the inequality |x+5|<4 is -9 < x < -1.

The integer values of x that satisfy this inequality are -8, -7, -6, -5, -4, -3, -2. So there are 7 different integer values of x that satisfy the inequality.