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Chapter 6: Problem 26

Solve each inequality and graph the solution set on a number line. \(8 x-4>12\)

Short Answer

Expert verified
The solution to the inequality \(8x - 4 > 12\) is \(x > 2\). The number line will have an open circle at 2, with an arrow pointing to the right, indicating all numbers greater than 2.

Step by step solution

01

Isolate the variable

Add 4 to both sides of the inequality to keep the equation balanced. This gives \(8x > 16\). Then, divide both sides of the equation by 8 to isolate \(x\), yielding \(x > 2\).
02

Indicate the solution on a number line

On a number line, a circle is drawn over 2, because 2 is not included in the solution (as \(x\) is strictly greater than 2). The circle is shown as not filled in. Draw an arrow to the right of 2, indicating all number greater than 2 are included in the solution set.

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Most popular questions from this chapter

Solve each equation by the method of your choice. \(7 x(x-2)=3-2(x+4)\)

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

Solve the equations using the quadratic formula. \(x^{2}-3 x=18\)

Solve the quadratic equations by factoring. \(x^{2}-2 x-15=0\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In an inequality such as \(5 x+4<8 x-5\), I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.
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