Question

Solve the equation 2m-3/2-m+1/3=3m-8/4

Answer 1

Concept:

Solution of an equation is the value(s) of the variable involved in that equation, for which the equation statement is true.

Given:

The given mathematical equation in this problem is 2m - 3/2 - m + 1/3 = 3m - 8/4

Find:

The solution or the value of the variable 'm' for the given above equation.

Solution:

Given mathematical equation is 2m - 3/2 - m + 1/3 = 3m - 8/4

On solving the given equation we get,

2m - 3/2 - m + 1/3 = 3m - 8/4

2m - 3/2 - m + 1/3 = 3m - 2

2m - m - 3m = 3/2 - 1/3 - 2, separating the variable and numbers

-2m = (3*3-1*2-2*6)/6, since LCM of 2,3 = 6

-2m = (9-2-12)/6

-2m = -5/6

2m = 5/6

m = 5/12

Hence the solution of given equation 2m - 3/2 - m + 1/3 = 3m - 8/4 is given by m = 5/12.

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Answer 2

Answer:

-10 is the required value of m.

Step-by-step explanation:

Explanation:

Given in the question that,

$\frac{2m - 3}{2} - \frac{m+1}{3} = \frac{3m - 8}{4}$

For this question first, we find out the lcm of 2 and 3, and then according to the BODMAS rule we solve it.

• Where LCM is the smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple (LCM), or smallest common multiple of two numbers a and b in mathematics and number theory.

Step 1:

From the question we have, $\frac{2m - 3}{2} - \frac{m+1}{3} = \frac{3m - 8}{4}$

Now, the LCM of 2 and 3 is 6.

⇒$\frac{3(2m -3)- 2(m+1)}{6}$ = $\frac{3m -8}{4}$

⇒$\frac{(6m -9)- (2m+2)}{6}$ = $\frac{3m -8}{4}$

⇒$\frac{(6m -9- 2m -2)}{6}$ = $\frac{3m -8}{4}$

⇒$\frac{4m - 11}{6} = \frac{3m - 8}{4}$

Now, by cross multiplication,

⇒ 4(4m - 11) = 6(3m - 8)

⇒16m - 44 = 18m - 24

⇒16m - 18m = -24 + 44 = 20

⇒-2m = 20

⇒m = $\frac{20}{-2}$ = -10

Final answer:

Hence, -10 is the required value of m.

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