Solve the following equations ) ((m-1))/2 – (( m-2))/3 = (( m-4 ))/7

Question

Solve the following equations ) ((m-1))/2 – (( m-2))/3 = (( m-4 ))/7

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Natalia 4 months 2021-08-01T10:46:48+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-01T10:48:01+00:00

    Answer:

    m – (m – 1)/2 = 1- (m – 2)/3

    (2m – m + 1)/2 = (3 – m + 2)/3

    (m + 1)/2 = ( 5 – m)/3

    3(m + 1) = 2(5 – m)

    3m + 3 = 10 – 2m

    3m + 2m = 10 – 3

    5m = 7

    m = 7/5

    Step-by-step explanation:

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    0
    2021-08-01T10:48:37+00:00

    Answer:

    \huge\boxed{m=-31}

    Step-by-step explanation:

    \dfrac{m-1}{2}-\dfrac{m-2}{3}=\dfrac{m-4}{7}\\\\LCM(2,\ 3,\ 7)=42\\\\42\!\!\!\!\!\diagup^{21}\cdot\dfrac{m-1}{2\!\!\!\!\diagup_1}-42\!\!\!\!\!\diagup^{14}\cdot\dfrac{m-2}{3\!\!\!\!\diagup_1}=42\!\!\!\!\!\diagup^6\cdot\dfrac{m-4}{7\!\!\!\!\diagup_1}\\\\21(m-1)-14(m-2)=6(m-4)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\(21)(m)+(21)(-1)+(-14)(m)+(-14)(-2)=(6)(m)+(6)(-4)\\\\21m-21-14m+28=6m-24\\\\\text{combine like terms}\\\\(21m-14m)+(-21+28)=6m-24

    7m+7=6m-24\qquad|\text{subtract}\ 6m\ \text{from both sides}\\\\m+7=-24\qquad\text{subtract 7 from both sides}\\\\m=-31

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