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Chapter 7: Problem 61

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed the solution set of \(y \geq x+2\) and \(x \geq 1\) without using test points.

Short Answer

Expert verified
The statement makes sense, because you can graph these inequalities without using test points. However, using test points can provide a more accurate solution.

Step by step solution

01

Understand the inequalities

The inequalities \(y \geq x+2\) and \(x \geq 1\) are both linear inequalities. The first one, \(y \geq x+2\), forms a line with a slope of 1 and a y-intercept at \(y=2\). The other inequality, \(x \geq 1\), is a vertical line crossing the x-axis at \(x=1\). Both inequalities include the boundary lines, symbolized by '\(\geq\)'. This means all the points lying on these lines are also part of the solution set.
02

Graph without using test points

One can graph the inequalities without using test points. For \(y \geq x+2\), all points above and on the line will satisfy the inequality. For the other inequality, \(x \geq 1\), all points to the right of, and on the line \(x=1\) will satisfy the inequality. The common region which satisfies both inequalities simultaneously will be the overall solution set.
03

Validate the statement

The statement makes sense because it's possible to graph the solution set of these two inequalities without using test points. However, it's better to use test points to make sure that the solution is accurate, especially when dealing with more complex inequalities.

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