Chapter 0.12, Problem 22E

To determine

Write the inequality and solve.

Answer to Problem 22E

x is the variable, $x+3<2x$ ; the number is $>3$

Explanation of Solution

Given:

Three more than a number is less than twice the number.

Concept Used:

Let the number be x.

Convert the question into an inequality equation.

Three more than a number is less than twice the number.

Three more than a number = $x+3$

less than twice the number = $<2x$

Inequality Equation: $x+3<2x$

Calculation:

Inequality Equation: $x+3<2x$

Solve for the variable x

  $\begin{array}{l}x+3<2x\\ x-2x+3<2x-2x\\ -x+3<0\\ -x+3-3<0-3\\ -x<-3\\ -1·-x>-1·-3\text{Multiply}\text{both}\text{sides}\text{by}-1\text{and}\text{reverse}\text{the}\text{inequality}\text{]}\\ x>3\end{array}$

  $\begin{array}{l}\text{Check}\text{the}\text{solution}\text{when}x=5\\ x+3<2x\\ 5+3<2·5\\ 8<10(\text{True}\text{statement})\end{array}$

Solution set: $(3,\infty )$

Thus, x is the variable and the inequality $x+3<2x$ ; the number is $>3$