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Chapter 6: Problem 62

Solve each inequality and graph the solution set on a number line. \(-6

Short Answer

Expert verified
The solution to the inequality is -2 < x <= 5 which is represented on a number line with an open circle at -2 and a closed circle at 5. The region between these two points is shaded to indicate all possible solutions.

Step by step solution

01

Isolate the variable x

Add 4 to all parts of the inequality to isolate x. This gives us: -6 + 4 < x - 4 + 4 <= 1 + 4. Simplifying, it becomes -2 < x <= 5.
02

Graph the solution set on a number line

Place a hollow circle at -2 since it is less than (-2 is not included), and a filled circle at 5 because it is less than or equal to (5 is included). Draw a line connecting the two points to represent all the numbers in between.

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Most popular questions from this chapter

Factor the trinomials in Exercises 9-32, or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+5 x+6\)

Solve the equations using the quadratic formula. \(4 x^{2}=12 x-9\)

Solve each equation by the method of your choice. \(\frac{x^{2}}{3}-\frac{x}{2}-\frac{3}{2}=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-7 x-44\)

Solve the quadratic equations by factoring. \(5 x^{2}+x=18\)
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