Question
upstudy study bank question image url

(Secre for Question 2: _of 5 points) 2. Solve the inequality \( -\frac{5}{2}(3 x+4)<6-3 x \). Show your work.

Ask by Cummings Potter. in the United States
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solution to the inequality is \( x > -\frac{32}{9} \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Mind Expander

To solve the inequality \( -\frac{5}{2}(3x + 4) < 6 - 3x \), let's start by distributing on the left side. 1. Distribute \( -\frac{5}{2} \): \[ -\frac{5}{2} \cdot 3x - \frac{5}{2} \cdot 4 < 6 - 3x \] This simplifies to: \[ -\frac{15}{2}x - 10 < 6 - 3x \] 2. Next, let's isolate \( x \). First, we'll move \( -3x \) to the left side and add \( 10 \) to both sides: \[ -\frac{15}{2}x + 3x < 6 + 10 \] Simplifying the right side gives us: \[ -\frac{15}{2}x + 3x < 16 \] Rewrite \( 3x \) as \( \frac{6}{2}x \) to combine like terms: \[ -\frac{15}{2}x + \frac{6}{2}x < 16 \] This simplifies to: \[ -\frac{9}{2}x < 16 \] 3. Now, divide both sides by \( -\frac{9}{2} \). Remember, when dividing by a negative number, the inequality sign flips: \[ x > \frac{16 \cdot 2}{9} \] This simplifies to: \[ x > \frac{32}{9} \] So, the solution to the inequality is: \[ x > \frac{32}{9} \] Now, onto some fun facts! In the early days of algebra, inequalities were not formally represented. Mathematicians like René Descartes and Nicolas Bourbaki helped formalize inequality notation. It wasn't until the 20th century that they gained the rigorous treatment we use today, complete with properties and theorems! In the real world, inequalities are everywhere! From economics—like comparing profits and costs—to planning a budget where you want expenses to stay below a certain threshold, inequalities help us understand constraints and make informed decisions. They can guide everything from business strategies to personal finance management!

Related Questions

Latest Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy