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Chapter 6: Problem 41

Solve each inequality and graph the solution set on a number line. \(3-7 x \leq 17\)

Short Answer

Expert verified
\(x \geq -2\)

Step by step solution

01

Isolate the negative term

Isolate the term with \(x\) on one side of the inequality by subtracting 3 from both sides. This gives: \(-7x \leq 17 - 3\). Simplifying this gives \(-7x \leq 14\)
02

Solve for \(x\)

Now divide both sides by -7 to isolate \(x\). This changes the direction of the inequality and gives: \(x \geq -2\)
03

Graph the solution

The solution can be represented on the number line by a closed dot at -2 because -2 is included in the solution. The portion of the line to the right of -2 should also be shaded because these values of \(x\) satisfy the inequality \(x \geq -2\)

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Most popular questions from this chapter

Explain how to solve a quadratic equation using the quadratic formula. Use the equation \(x^{2}+6 x+8=0\) in your explanation.

The radicand of the quadratic formula, \(b^{2}-4 a c\), can be used to determine whether \(a x^{2}+b x+c=0\) has solutions that are rational, irrational, or not real numbers. Explain how this works. Is it possible to determine the kinds of answers that one will obtain to a quadratic equation without actually solving the equation? Explain.

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(6 x^{2}-17 x+12\)

Solve each equation by the method of your choice. \((2 x-6)(x+2)=5(x-1)-12\)

Solve the equations in Exercises 53-72 using the quadratic formula. \(x^{2}+8 x+15=0\)
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