Question

SOLVING INEQUALITIES Solve the inequality. $$-2 x-y \geq 4$$

Short answer

The solution to the inequality \(-2x - y \geq 4\) is \(y \leq -2x - 4\).

Step-by-step solution

Rearrange the inequality

The first aim is to isolate \(y\). We start by moving \(-2x\) to the right side by adding \(2x\) to both sides of the inequality. The inequality now becomes \( -y \geq 4 + 2x \).

Isolate y

Now, we want to get rid of the negative sign in front of \( y \). We can do this by multiplying the entire inequality by \(-1\). But we remember that when we multiply or divide an inequality by a negative number, the direction of the inequality changes. The inequality now becomes \( y \leq -4 -2x \).

Rearrange the terms

For a clearer presentation, we can rearrange the right-hand side by placing the \(x\) term before the constant. This brings us to the final inequality: \( y \leq -2x -4 \).