Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
Given Question
Solve for x :
[tex]\rm :\longmapsto\:\dfrac{3x - 5}{2} + x + \dfrac{2x - 3}{3} = \dfrac{5}{6} - \dfrac{3x}{2} [/tex]
[tex] \green{\large\underline{\sf{Solution-}}}[/tex]
Given expression is
[tex]\rm :\longmapsto\:\dfrac{3x - 5}{2} + x + \dfrac{2x - 3}{3} = \dfrac{5}{6} - \dfrac{3x}{2} [/tex]
- On taking LCM of (2 and 3 = 6) on LHS and Taking LCM of ( 2 and 6 = 6) on RHS, we get
[tex]\rm :\longmapsto\:\dfrac{3(3x - 5) + 6x + 2(2x - 3)}{6} = \dfrac{5 - 9x}{6}[/tex]
[tex]\rm :\longmapsto\:9x - 15 + 6x + 4x - 6 = 5 - 9x[/tex]
[tex]\rm :\longmapsto\:(9x + 6x + 4x) - 15 - 6 = 5 - 9x[/tex]
[tex]\rm :\longmapsto\:19x - 21 = 5 - 9x[/tex]
[tex]\rm :\longmapsto\:19x + 9x = 5 + 21[/tex]
[tex]\rm :\longmapsto\:28x = 26[/tex]
[tex]\rm :\longmapsto\:x = \dfrac{26}{28} [/tex]
[tex]\bf\implies \:x = \dfrac{13}{14} [/tex]
VERIFICATION
Consider LHS
[tex]\rm :\longmapsto\:\dfrac{3x - 5}{2} + x + \dfrac{2x - 3}{3}[/tex]
On substituting the value of x, we get
[tex]\rm \: = \: \dfrac{\dfrac{39}{14} - 5}{2} + \dfrac{13}{14} + \dfrac{\dfrac{13}{7} - 3}{3}[/tex]
[tex]\rm \: = \: \dfrac{39- 70}{28} + \dfrac{13}{14} + \dfrac{13 - 21}{21}[/tex]
[tex]\rm \: = \: \dfrac{ - 31}{28} + \dfrac{13}{14} - \dfrac{8}{21}[/tex]
[tex]\rm \: = \: \dfrac{ - 31 + 26}{28} - \dfrac{8}{21}[/tex]
[tex]\rm \: = \: \dfrac{ -5}{28} - \dfrac{8}{21}[/tex]
[tex]\rm \: = \: \dfrac{ -15 - 32}{84}[/tex]
[tex]\rm \: = \: - \: \dfrac{47}{84}[/tex]
Consider RHS
[tex]\rm :\longmapsto\: \dfrac{5}{6} - \dfrac{3x}{2} [/tex]
On substituting the value of x, we get
[tex] \rm \: = \: \dfrac{5}{6} - \dfrac{39}{28} [/tex]
[tex] \rm \: = \: \dfrac{70 - 117}{84}[/tex]
[tex] \rm \: = \: - \dfrac{47}{84}[/tex]
Hence, LHS = RHS
Hence, Verified.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.