Question

2Try It! Solve anInequality With Variables on Both Sides2. Solve 2x - 5 < 5x - 22. Then graph the solution

Answer 1

You have to solve the following inequality:

`2x-5<5x-22`

To solve an inequality the method is similar as when you are solving an equation.

First, using addition/subtraction rearrange the terms so that all x-related terms end up in one side of the expression and the constants remain in the other side:

First add 5 to both sides of the inequality and solve:

`\begin{gathered} 2x-5+5<5x-22+5 \\ 2x<5x-17 \end{gathered}`

Next subtract 5x to both sides and solve:

`\begin{gathered} 2x-5x<5x-5x-17 \\ -3x<-17 \end{gathered}`

Finally you have to divide both sides by -3 to determine the possible value of x.

Be careful, when you are solving an inequality and divide it by a negative number, do not forget that this operation changes the direction of the inequality, this means that if the original inequality had the "<" symbol, after dividing by the negative number the symbol will be ">"

`\begin{gathered} -(3x)/(-3)>-(17)/(-3) \\ x>(17)/(3) \end{gathered}`

The solution of this inequality are all values greater than 17/3