Question

Define a variable and write an inequality for each problem. Then solve.

12. The product of 12 and a number is greater than 36.

Short answer

Let the variable number be $x$

Inequality is $12x>36$

Solution is $x>3$

Step-by-step solution

-Write an inequality

Let the number whose product with 12 is greater than 36 be $x$

Thus, inequality is

$\begin{array}{c}12\times x>36\\ 12x>36\end{array}$

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify 12x>36

To simplify given inequality, use division property of inequalities. Divide both sides by same positive number does not reverse the sign of inequality as shown below

$\begin{array}{c}12x>36\\ \frac{12x}{12}>\frac{36}{12}\\ x>3\end{array}$

Thus, solution is $x>3$