Login
Premium
Home Question Bank Math Algebra
Question
upstudy study bank question image url

- \( 5 x+9-x \leq 6-2 x \)

Ask by Chambers Lewis. in Dominican Republic
Jan 30,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

La solución es \( x \leq -\frac{1}{2} \).

Solution

Para resolver la desigualdad \( 5x + 9 - x \leq 6 - 2x \), seguiremos los siguientes pasos: 1. **Simplificar términos semejantes en ambos lados de la desigualdad:** \[ 5x - x + 9 \leq 6 - 2x \] \[ 4x + 9 \leq 6 - 2x \] 2. **Reunir las variables en un lado y las constantes en el otro lado. Para ello, sumamos \( 2x \) a ambos lados:** \[ 4x + 2x + 9 \leq 6 \] \[ 6x + 9 \leq 6 \] 3. **Restar 9 a ambos lados para aislar el término con \( x \):** \[ 6x + 9 - 9 \leq 6 - 9 \] \[ 6x \leq -3 \] 4. **Dividir ambos lados por 6 para despejar \( x \):** \[ \frac{6x}{6} \leq \frac{-3}{6} \] \[ x \leq -\frac{1}{2} \] **Solución final:** \[ x \leq -\frac{1}{2} \] Esto significa que todos los valores de \( x \) que sean menores o iguales a \(-\frac{1}{2}\) satisfacen la desigualdad original.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Beyond the Answer

To solve the inequality \( 5x + 9 - x \leq 6 - 2x \), start by simplifying the left side. Combine like terms: \( 4x + 9 \leq 6 - 2x \). Next, add \( 2x \) to both sides to isolate \( x \): \( 4x + 2x + 9 \leq 6 \), which simplifies to \( 6x + 9 \leq 6 \). Now, subtract 9 from both sides: \( 6x \leq -3 \). Finally, divide by 6: \( x \leq -\frac{1}{2} \). So, the solution set includes all values of \( x \) that are less than or equal to -0.5. --- Using a step-by-step approach makes solving inequalities a breeze, but make sure to keep an eye out for signs when multiplying or dividing by a negative number, as that changes the direction of the inequality. These small slips can trip you up when you're racing towards the finish line! If you’re interested in brushing up on inequalities, consider diving into algebraic tricks, such as balancing equations or mastering the properties of inequalities—you'll be handling these like a pro in no time!

Related Questions

Divide. \[ \left(12 x^{3}-24 x^{2}+6 x+10\right) \div\left(3 x^{2}-3 x\right) \] Your answer should give the quotient and the remainder. Quotient: \( \square \) Remainder: \( \square \)
Algebra United States Feb 20, 2025
\[ \left(3 x^{2}+26 x+36\right) \div(x+7) \] Your answer should give the quotient and the remainder. Quotient: \( \square \) Remainder: \( \square \)
Algebra United States Feb 20, 2025
Divide. \[ \left(14 x+20 x^{3}+11+15 x^{2}\right) \div\left(5 x^{2}+2\right) \] Write your answer in the following form: Quotient \( +\frac{\text { Remainder }}{5 x^{2}+2} \). \( \frac{14 x+20 x^{3}+11+15 x^{2}}{5 x^{2}+2}=\square+\frac{\square}{5 x^{2}+2}+\square \times \square \)
Algebra United States Feb 20, 2025
\( 3 y+x=2 \) and \( y^{2}+x=x y+y \)
Algebra South Africa Feb 20, 2025
(8) \( 3^{-x}=\frac{1}{243} \)
Algebra South Africa Feb 20, 2025

Latest Algebra Questions

Activity 4 4.1 Consider the linear sequence: \( 5 ; 8 ; 11 ; b: 17: \ldots \) 4.1.1 Write down the value of \( b \). 4.1.2 Determine the \( n^{t h} \) term of the sequence. 4.1.3 Calculate the value of the \( 15^{\oplus} \) term of the sequence. 4.1.4 Which term of the sequence is equal to 83 ? Activity 5 5.1 The first term of a linear number pattern is 92 and the constant difference is -4 . 5.1.1 Write down the values of the second and third terms of the pattern. 5.12 Determine an expression for the \( n^{\text {th }} \) term of the number patterm. 5.13 Determine the value of the eighteenth term. S.1.4 If \( T_{p}+T_{q}=0 \), determine the value of \( (p+q) \). TUTORLAL 2 Activity 1 1.1 Given the finite linear number pattern: \( 12 ; 17 ; 22 ; 22 ; \ldots ; 172 \). 1.1.1 Deternine the formula \( n^{\text {th }} \) term of the pattern. 1.1.2 Calculate the value of \( T_{12} \). 1.1.3 Deternine the number of terms in the pattern. 12 Given the first four terms of a linear pattern: \( 3: x: y: 30 \)
Algebra South Africa Feb 20, 2025
5. MP Use Tools Write an expression with a single exponent that is equivalent to \( 8^{-4} \cdot\left(8^{2}\right)^{4} \). State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.
Algebra United States Feb 20, 2025
Divide. \[ \left(14 x+20 x^{3}+11+15 x^{2}\right) \div\left(5 x^{2}+2\right) \] Write your answer in the following form: Quotient \( +\frac{\text { Remainder }}{5 x^{2}+2} \). \( \frac{14 x+20 x^{3}+11+15 x^{2}}{5 x^{2}+2}=\square+\frac{\square}{5 x^{2}+2}+\square \times \square \)
Algebra United States Feb 20, 2025
22. Дадени са числата \( x \) и \( y \), като: (1) \( x \) е неизвестно число в равенството \( 3^{-2}: x-2 \frac{4}{5}=\left(-\frac{3}{10}\right)^{7} \cdot\left(3 \frac{1}{3}\right)^{7}-0,8 \); 2) \( y \) е такова, че стойността на израза \( 3 \cdot y-\left|\frac{-8-\left(-2^{2}\right)}{8}\right| \) е с 4 по-голяма от стойността на израза \( \frac{1}{2} \) . Намерете \( x \). . Намерете \( y \). С Солко \( x \) е по-малко от \( y \) ? С С колко процента \( y \) е по-голямо от \( x \) ? Намерете стойността на израза \( x^{y-3} \cdot\left(\frac{x-y}{3}\right) \).
Algebra Bulgaria Feb 20, 2025
\( 3 y+x=2 \) and \( y^{2}+x=x y+y \)
Algebra South Africa Feb 20, 2025
Prev Next
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