Question

solve for x and graph the solution.
2x² + 8x - 10 ≥ 0
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Explanation:

Step1: Simplify the inequality

Divide the inequality \(2x^{2}+8x - 10\geq0\) by \(2\) to get \(x^{2}+4x - 5\geq0\).

Step2: Factor the quadratic

Factor \(x^{2}+4x - 5\) as \((x + 5)(x-1)\geq0\).

Step3: Find the roots

Set \((x + 5)(x - 1)=0\). Using the zero - product property \(x+5 = 0\) gives \(x=-5\), and \(x - 1=0\) gives \(x = 1\).

Step4: Test intervals

• For \(x<-5\), let \(x=-6\). Then \((-6 + 5)(-6-1)=(-1)\times(-7)=7\geq0\).
• For \(-5
• For \(x>1\), let \(x = 2\). Then \((2 + 5)(2-1)=(7)\times(1)=7\geq0\).

Answer:

The solution of the inequality \(2x^{2}+8x - 10\geq0\) is \(x\leq - 5\) or \(x\geq1\). On the number - line, we plot closed circles (since the inequality is \(\geq\)) at \(x=-5\) and \(x = 1\). The graph consists of two rays: one from \(-\infty\) to \(-5\) (including \(-5\)) and one from \(1\) to \(\infty\) (including \(1\)).