Question

solve the inequality and graph the solution.
\\(\frac{j}{-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.
(number line with -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 marked)

Explanation:

Step1: Isolate the fraction term

Start with the inequality \(\frac{j}{-2}-1\geq1\). Add 1 to both sides to isolate the fraction:
\(\frac{j}{-2}-1 + 1\geq1 + 1\)
Simplify: \(\frac{j}{-2}\geq2\)

Step2: Solve for \(j\)

Multiply both sides by \(-2\). Remember: when multiplying or dividing an inequality by a negative number, reverse the inequality sign.
\(\frac{j}{-2}\times(-2)\leq2\times(-2)\)
Simplify: \(j\leq - 4\)

Graphing the Solution:

• The endpoint is at \(j = - 4\) (closed circle, since the inequality is \(\leq\)).
• The arrow points to the left (towards smaller numbers) to represent all values \(j\leq - 4\).

Answer:

The solution to the inequality is \(j\leq - 4\). For the graph, plot a closed circle at \(-4\) and draw an arrow to the left.