Chapter 5: Q26. (page 302)

Define a variable, write an inequality, and solve each problem. Check your solution.
Two thirds of a number plus 5 is greater than 17.

Short Answer

Expert verified

The variable is x is and the inequality equation is $\frac{2}{3} x + 5 > 17$ . The solution for the inequality is $x > 18$ .

Step by step solution

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\leq or \geq$ , use the bracket or a solid circle at that endpoint.

Properties of inequality:

width="189">1.b≤c⇒b±a≤c±a2.b≤c⇒ab≤ac,ifa>03.b≤c⇒ab≥ac,ifa<0

Step 2. Write the inequality for the given condition.

Let the number be x.

Two thirds of a number plus 5 is greater than 17:

$\frac{2}{3} x + 5 > 17$

Step 3. Solve for x.

Solve for x in the inequation $\frac{2}{3} x + 5 > 17$

$\frac{2}{3} x + 5 > 17 \frac{2}{3} x + 5 - 5 > 17 - 5 \frac{2}{3} x > 12 \frac{2}{3} x \times 3 > 12 \times 3 2 x > 36 \frac{2 x}{2} > \frac{36}{2} x > 18$

Step 4. Check the solution.

Put the value of xas 20

$\frac{2}{3} x + 5 > 17 \frac{2}{3} (21) + 5 > 17 14 + 5 > 17 19 > 17 [TrueStatement]$

Thus, the solution of the inequality equation $\frac{2}{3} x + 5 > 17$ is $x > 18$ .

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Define a variable, write an inequality, and solve each problem. Check your solution.
Two thirds of a number plus 5 is greater than 17.

Short Answer

Step by step solution

Step 1. State the concept for inequality.

Step 2. Write the inequality for the given condition.

Step 3. Solve for x.

Step 4. Check the solution.

One App. One Place for Learning.

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Define a variable, write an inequality, and solve each problem. Check your solution.Two thirds of a number plus 5 is greater than 17.

Short Answer

Step by step solution

Step 1. State the concept for inequality.

Step 2. Write the inequality for the given condition.

Step 3. Solve for x.

Step 4. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Define a variable, write an inequality, and solve each problem. Check your solution.
Two thirds of a number plus 5 is greater than 17.