[tex]\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[/tex]
[tex]7m+7=6m-24\qquad|\text{subtract}\ 6m\ \text{from both sides}\\\\m+7=-24\qquad\text{subtract 7 from both sides}\\\\m=-31[/tex]
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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Answer:
[tex]\huge\boxed{m=-31}[/tex]
Step-by-step explanation:
[tex]\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[/tex]
[tex]7m+7=6m-24\qquad|\text{subtract}\ 6m\ \text{from both sides}\\\\m+7=-24\qquad\text{subtract 7 from both sides}\\\\m=-31[/tex]