62.3k views
1 vote
Solve the inequality. Write the solution in both interval notation and graphically.

Solve the inequality. Write the solution in both interval notation and graphically-example-1
User Brad Leach
by
8.0k points

1 Answer

2 votes

Given:


(3)/(4)(x-2)\text{ }<\text{ x -2}

Opening the bracket:


(3x)/(4)\text{ - }(6)/(4)\text{ }<\text{ x - 2}

Collect like terms:


\begin{gathered} (3x)/(4)-x\text{ }<\text{ }(6)/(4)\text{ - 2} \\ (3x-4x)/(4)\text{ }<\text{ }(6-8)/(4) \\ -(x)/(4)\text{ }<\text{ }(-2)/(4) \end{gathered}

Solving for x:


\begin{gathered} -(x)/(4)\text{ }<\text{ }(-2)/(4) \\ -x\text{ }<\text{ -2} \\ x\text{ > 2} \end{gathered}

The solution in interval notation:


(2\text{ , }\infty\text{ )}

The solution on a graph:

The solution on a number line:

Solve the inequality. Write the solution in both interval notation and graphically-example-1
Solve the inequality. Write the solution in both interval notation and graphically-example-2
User Makavelli
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories