Q3. - Algebra 2

Question

FIND THE ERROR

Sabrina and Isaac are solving $|3x+7|>2$

Who is correct? Explain your reasoning.

Step-by-Step Solution

Answer

From definition of absolute value inequality, Sabrina use correct definition, so her answer is correct. But one inequality $3x>25$ in her steps is incorrect.

Step 1 - Definition of absolute value inequality

For real numbers $a\text{ and }b$ with $b>0$ 

Absolute value inequality is $\left|a\right|<b$ when $-b<a\text{ and }a<b$, and

Absolute value inequality is $\left|a\right|>b$ when $a<-b\text{ or }a>b$ 

Step 2 - Write properties of inequality

Properties of inequalities are written in following table:

Step 3 - Simplify 3 x + 7 &#62; 2

From definition of absolute value inequality, given expression is simplified to 

$3x+7>2\text{ or }3x+7<-2$ 

Use subtraction and division property of inequality, subtract with same number does not change the sign of inequality. Also division by same positive number does not reverse the sign of inequality as shown below

$\begin{array}{c}3x+7-7>2-7\text{ or }3x+7-7<-2-7\\ 3x>-5\text{ or }3x<-9\\ \frac{3x}{3}>-\frac{5}{3}\text{ or }\frac{3x}{3}<-\frac{9}{3}\\ x>-\frac{5}{3}\text{ or }x<-3\end{array}$

Step 4 - Check whose solution is correct

From definition of absolute value inequality, Sabrina use correct definition, so her answer is correct. But one inequality 3x>25 in her steps is incorrect.