Graph each inequality. x ≤ 3

Question

Accepted Answer

Hello everybody. And I today today we're going to be talking about this question that stays draw the graph for the given inequality where the inequality is X is less than or equal to five. Now, the first thing I'll do for the sake of the graph is I'll just replace the best in or equal to sign with an equal sign just to have X is equal to five. And this is the graph that we will draw. Now, a note for our inequality is that it is a non strict inequality, meaning that we have a less than or equal to sign if we didn't have that equal to, if it was just less than this would be a strict inequality and it would affect our graph, as I'll mention later on. Now, for the graph of X equals five, we can just go ahead and graph that. So we'll draw a Y axis and then X axis and will draw a dash at the five. And we know that the graph of an X equals five is simply going to be a vertical line, going up and down straight on the value X equals five. So at the 50.5 comma zero. So because we have an inequality that was not strict, we use a solid line and that is the point of keeping track of what type of inequality we have. Now, we know we're gonna have to shade a specific region. So for that, we'll test a point and in this case, we'll test the 0.0 comma zero. And to do that, we'll just plug in that point into our equation where our equation is X is less than or equal to five. So we plug in zero for our X, we'll have that zero is less than or equal to five. And this is true. Therefore, the 0.0 comma zero would work and we can shade in the region to the left of our vertical line. If that point didn't work, that means we have to shade in the other region to the right. And just like that, we will obtain a graph for our inequality. We have a vertical line at X equals five with a shaded region to the left of it. So I hope that was helpful. And until next time.

Graph each inequality. x ≤ 3

Key Concepts

Inequalities

Graphing on a Number Line

Closed and Open Intervals

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