Question

solve the following equation ​

Answer 1

Question: If x = m + 1, find the value of m from the equation $\tt \dfrac{1}{2}(5x-6)- \dfrac{1}{3}(1+7x)= \dfrac{1}{2}$

Answer:

$\huge{\underline{\boxed{\red{\bf m=22}}}}$

Step-by-step explanation:

Solving the above equation,

$: \implies \tt \dfrac{1}{2}(5x-6)- \dfrac{1}{3}(1+7x)= \dfrac{1}{2}$

$: \implies \tt \dfrac{5x-6}{2} - \dfrac{1 +7x}{3} =\dfrac{1}{2}$

Taking LCM of the denominators,

$: \implies \tt \dfrac{3(5x-6)-2(1+7x)}{6}=\dfrac{1}{2}$

$: \implies \tt \dfrac{15x-18-2-14x}{6}=\dfrac{1}{2}$

$: \implies \tt \dfrac{x-20}{6}=\dfrac{1}{2}$

On cross-multiplying,

$: \implies \tt 2(x-20)=6$

$: \implies \tt x - 20 = \dfrac{6}{2}$

$: \implies \tt x - 20 = 3$

$: \implies \tt x = 3 + 20$

$\boxed{\bf \therefore x = 23}$

Now, it is given that ;

$: \implies \sf x = m + 1$

$: \implies \sf m = x - 1$

$: \implies \sf m = 23-1$

$\large{\underline{\boxed{\bf \therefore m = 22}}}$

Hence, the value of m is 22.

Answer 2

Given:-

• $\sf{x = m + 1}$

• $\sf{\dfrac{1}{2}(5x - 6) - \dfrac{1}{3}(1 + 7x) = \dfrac{1}{2}}$

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To find:-

• Value of m.

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Solution:-

$\large{\tt{\longmapsto{\dfrac{1}{2}(5x - 6) - \dfrac{1}{3}(1 + 7x) = \dfrac{1}{2}}}}$

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$\large{\tt{\longmapsto{\dfrac{1}{2} [5m + 5 - 6] - \dfrac{1}{3} [1 + 7(m + 1)] = \dfrac{1}{2}}}}$

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$\large{\tt{\longmapsto{\dfrac{1}{2} [5m + 5 - 6] - \dfrac{1}{3} [1 + 7m + 7)] = \dfrac{1}{2}}}}$

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$\large{\tt{\longmapsto{\dfrac{1}{2} [5m - 1] - \dfrac{1}{3} [7m + 8)] = \dfrac{1}{2}}}}$

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$\large{\tt{\longmapsto{\dfrac{5m - 1}{2} - \dfrac{7m + 8}{3} = \dfrac{1}{2}}}}$

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★ Taking LCM:-

$\large{\tt{\longmapsto{\dfrac{3(5m - 1) - 2(7m + 8)}{6} = \dfrac{1}{2}}}}$

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$\large{\tt{\longmapsto{\dfrac{15m - 3 - 14m - 16}{6} = \dfrac{1}{2}}}}$

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$\large{\tt{\longmapsto{\dfrac{m - 19}{6} = \dfrac{1}{2}}}}$

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$\large{\tt{\longmapsto{m - 9 = \dfrac{6}{2} = 3}}}$

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$\large{\tt{\longmapsto{m = 3 + 19}}}$

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$\boxed{\large{\tt{\longmapsto{\purple{m = 22}}}}}$

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