Question

5/8(m-2)-2/3(m+2)=m-3

Answer 1

5/8(m-2)-2/3(m+2)=m-3

5/8m-5/4-2/3m-4/3=m-3

5/8m-31/12-2/3m=m-3

15m-62-16m=24m-72

-m-62=24m-72

-m-24m=-72+62

-25m=-10

25m=10

m=2/5=0.4

Answer 2

To solve the equation $\frac{5}{8}(m-2) - \frac{2}{3}(m+2) = m-3$, follow these steps:

Step 1: Distribute the fractions on both sides of the equation: $\frac{5}{8}(m) - \frac{5}{8}(2) - \frac{2}{3}(m) - \frac{2}{3}(2) = m - 3$

Step 2: Multiply the fractions with their respective terms: $\frac{5}{8}m - \frac{5}{4} - \frac{2}{3}m - \frac{4}{3} = m - 3$

Step 3: Get rid of the fractions by finding a common denominator. In this case, the common denominator is 24.

$\frac{15}{24}m - \frac{30}{24} - \frac{16}{24}m - \frac{32}{24} = m - 3$

Step 4: Combine like terms on both sides of the equation:

$\left(\frac{15}{24}m - \frac{16}{24}m\right) - \left(\frac{30}{24} + \frac{32}{24}\right) = m - 3$

$\frac{-1}{24}m - \frac{62}{24} = m - 3$

Step 5: To isolate the variable "m," add $\frac{1}{24}m$ to both sides of the equation:

$\frac{-1}{24}m + \frac{1}{24}m - \frac{62}{24} = m - 3 + \frac{1}{24}m$

Simplify:

$-\frac{62}{24} = m - 3 + \frac{1}{24}m$

Step 6: Add 3 to both sides of the equation to isolate "m":

$-\frac{62}{24} + 3 = m - 3 + \frac{1}{24}m + 3$

Simplify:

$-\frac{62}{24} + \frac{72}{24} = \frac{1}{24}m + m$

$\frac{10}{24} = \frac{25}{24}m$

Step 7: Divide both sides by $\frac{25}{24}$ to solve for "m":

$\frac{10}{24} \div \frac{25}{24} = \frac{25}{24}m \div \frac{25}{24}$

Simplify:

$\frac{10}{25} = m$

$\frac{2}{5} = m$

So, the solution to the equation is $m = \frac{2}{5}$