Question

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

Three less than twice a number is at most 5.

Short answer

Let the variable number be x

Inequality is $2x-3\le 5$

Solution is $x\le 4$

Step-by-step solution

-Write an inequality

Let the required number be x

As 3 less than 2 times of x is at most 5

Thus, inequality is

$2x-3\le 5$

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify 2x−3≤5

To simplify given inequality, use addition and division property of inequalities, Add same number on both sides does not change the sign of inequality. Also divide both sides by same positive number does not reverse the sign of inequality as shown below

$\begin{array}{c}2x-3\le 5\\ 2x-3+3\le 5+3\\ \frac{2x}{2}\le \frac{8}{2}\\ x\le 4\end{array}$

Thus, solution is $x\le 4$