Question

graph the values of x that satisfy the given conditions. x ≤ -15 or x ≥ 25. choose the correct graph below. a. graph with -25, -15 (filled - in circle), 0, 25 (filled - in circle), 45 on number line and arrows pointing left from -15 and right from 25 b. graph with -25, -15 (open circle), 0, 25 (open circle), 45 on number line and arrows pointing left from -15 and right from 25 c. graph with -25, -15 (open circle), 0, 25 (open circle), 45 on number line and a line segment between -15 and 25 d. graph with -25, -15 (filled - in circle), 0, 25 (filled - in circle), 45 on number line and a line segment between -15 and 25

Explanation:

Step1: Analyze inequality signs

The inequality $x\leq - 15$ includes -15 and all values less than -15. The inequality $x\geq25$ includes 25 and all values greater than 25. Closed - circles are used for $\leq$ and $\geq$ on the number - line graph.

Step2: Check each option

Option A has closed - circles at -15 and 25 and the correct shaded regions for $x\leq - 15$ and $x\geq25$. Option B has open - circles which is incorrect for the given $\leq$ and $\geq$ inequalities. Option C has open - circles and incorrect shading. Option D has incorrect shading as it shows the region between -15 and 25 instead of the regions $x\leq - 15$ or $x\geq25$.

Answer:

A.