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Chapter 6: Problem 12

Graph each set of real numbers on a number line. \(\\{x \mid-7 \leq x \leq 0\\}\)

Short Answer

Expert verified
The set of numbers from -7 to 0, including -7 and 0, is represented on the number line by a filled line segment from -7 to 0. The ends at -7 and 0 are filled (or 'closed') to show that these numbers are included in the set.

Step by step solution

01

Understand the set

The set contains all the real numbers \(x\) that are greater than or equal to -7 and less than or equal to 0. This can be described as a closed interval, \([-7, 0]\).
02

Sketch the number line

Draw a straight horizontal line, this will represent the number line. It represents all possible real numbers. Mark points for -7, 0 and a few other representative values around them on the line.
03

Mark the interval

Since -7 and 0 are included in the set (as indicated by the \'\leq\' symbol), fill in a solid circle at -7 and 0. Draw a line connecting these two points to represent all the numbers between them.

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Most popular questions from this chapter

Use FOIL to find the products. \((x-5)(x+3)\)

Solve the equations using the quadratic formula. \(6 x^{2}-5 x-6=0\)

Solve the quadratic equations by factoring. \(x^{2}+5 x+6=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-8 x+15\)

Solve each equation using the zero-product principle. \((4 x+5)(x-2)=0\)
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