Solve
1) 2x+7/5 - 3x+11/2 = 2x+8/3 - 5
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Answer:
Taking all x variables on one side
2x -3x-2x =-7/5-11/2+8/3-5
solving..LCM
-3x=(-42-165+80-150)/30
-3x=-277/30
x=277/90
x=3.07
Verified answer
Answer:
[tex]\qquad\qquad\qquad\boxed{ \sf{ \: \sf \: x = - 1 \: }}\\ \\ [/tex]
Step-by-step explanation:
Given linear equation is
[tex]\sf \: \dfrac{2x + 7}{5} - \dfrac{3x + 11}{2} = \dfrac{2x + 8}{3} - 5 \\ \\ [/tex]
[tex]\sf \: \dfrac{2(2x + 7) - 5(3x + 11)}{10} = \dfrac{2x + 8 - 15}{3} \\ \\ [/tex]
[tex]\sf \: \dfrac{4x + 14 - 15x - 55}{10} = \dfrac{2x - 7}{3} \\ \\ [/tex]
[tex]\sf \: \dfrac{ - 11x - 41}{10} = \dfrac{2x - 7}{3} \\ \\ [/tex]
[tex]\sf \: 3( - 11x - 41) = 10(2x - 7) \\ \\ [/tex]
[tex]\sf \: - 33x - 123 = 20x - 70 \\ \\ [/tex]
[tex]\sf \: - 33x - 20x = 123 - 70 \\ \\ [/tex]
[tex]\sf \: - 53x = 53 \\ \\ [/tex]
[tex]\sf \: x = \frac{53}{ - 53} \\ \\ [/tex]
[tex]\sf\implies \sf \: x = - 1 \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]