Question

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

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 $\le \text{or}\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

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

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

Step 4. Check the solution.

Put the value of xas 20

$$\begin{gathered} \frac{2}{3}x+5>17 \\ \frac{2}{3}\left(21\right)+5>17 \\ 14+5>17 \\ 19>17\left[\text{TrueStatement}\right] \end{gathered}$$

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