Solve the absolute value inequality |𝑥+2|≥4

To solve the absolute value inequality |𝑥+2|≥4, we need to set up two separate inequalities because the expression inside the absolute value can be either positive or negative.

1. The first inequality is (𝑥+2) ≥ 4. To solve for x, we subtract 2 from both sides of the inequality, which gives us 𝑥 ≥ 4 - 2, or 𝑥 ≥ 2.

2. The second inequality is -(𝑥+2) ≥ 4. To solve for x, we first remove the negative sign by multiplying both sides of the inequality by -1. Remember that when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign changes. So, we get 𝑥+2 ≤ -4. Then, we subtract 2 from both sides of the inequality, which gives us 𝑥 ≤ -4 - 2, or 𝑥 ≤ -6.

So, the solution to the absolute value inequality |𝑥+2|≥4 is 𝑥 ≥ 2 or 𝑥 ≤ -6.