Chapter 8.8, Problem 56HP

To determine

Her mistake and correct it

Answer to Problem 56HP

The solution of the inequality is $x\ge -29.5$

Mistake is Jada did not multiply by 5 in distributed property

Explanation of Solution

Given:

The inequality, $3x-9\le 5\left(x+10\right)$

  

Concept used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• Inequality sign get reverse on multiplying or dividing by a negative number

Calculation:

• In order to solve the mixed inequality $3x-9\le 5\left(x+10\right)$ first isolate the variable term x by performing some basic operations. Here to isolate x terms on the left side, first use distributive property and then add both sides by $9$ and then divide both sides by $-5$ and then Inequality sign get reverse on multiplying or dividing by a negative number and then simplify further as shown below:

  $\begin{array}{c}3x-9\le 5\left(x+10\right)\\ 3x-9\le 5\cdot x+5\cdot 10\\ 3x-9\le 5x+50\\ 3x-9-5x\le 5x+50-5x\\ -2x-9\le 50\\ -2x-9+9\le 50+9\\ -2x\le 59\\ \frac{-2x}{-2}\ge \frac{59}{-2}\\ x\ge -29.5\end{array}$

Thus, the solution of the given inequality is $x\ge -29.5$ .

Mistake is Jada did not multiply by 5 in distributed property