Question

solve the inequality and graph the solution.
\\( \frac { u } { - 2 } - 1 \geq 1 \\)
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
submit

Explanation:

Step1: Add 1 to both sides

$$\frac{u}{-2}-1 + 1\geq1 + 1$$
$$\frac{u}{-2}\geq2$$

Step2: Multiply both sides by -2 (and reverse the inequality sign)

When multiplying or dividing an inequality by a negative number, the inequality sign flips.
$$\frac{u}{-2}\times(-2)\leq2\times(-2)$$
$$u\leq - 4$$

Answer:

The solution of the inequality is \(u\leq - 4\). On the number - line, we plot a closed circle at \(-4\) (because the inequality includes equality, \(\geq\) after manipulation becomes \(\leq\) and the original variable \(u\) satisfies \(u = - 4\) is part of the solution) and draw an arrow to the left.