Question

2m+7/4(3/4m-5/2)=3/32+1/3m

Answer 1

For this case we have the following equation:

`2m + \frac {7} {4} (\frac {3} {4} m- \frac {5} {2}) = \frac {3} {32} + \frac {1} {3} m`

We apply distributive property on the left side of the equation:

`2m + \frac {21} {16} m- \frac {35} {8} = \frac {3} {32} + \frac {1} {3} m`

We add similar terms from the left side:

`\frac {53} {16} m- \frac {35} {8} = \frac {3} {32} + \frac {1} {3} m`

Add
`\frac {35} {8}`to both sides:

`\frac {53} {16} m = \frac {3} {32} + \frac {1} {3} m + \frac {35} {8}`

We subtract
`\frac {1} {3} m` from both sides:

`\frac {53} {16} m- \frac {1} {3} m = \frac {3} {32} + \frac {35} {8}\\\frac {143} {48} m = \frac {1144} {256}\\143m = \frac {1144 * 48} {256}`

We simplify:

`143m=(54912)/(256)\\143m=(13728)/(64)\\143m=(3432)/(16)\\143m=(858)/(4)\\143m=(429)/(2)`

We divide between 143 on both sides:

`m=(429)/(2*143)\\m=(429)/(286)\\m=(33)/(22)\\m=(3)/(2)`

ANswer:

`m=(3)/(2)`

Answer 2

Answer:
`m=(3)/(2)`

Step-by-step explanation:

We have the following equation:

`2m+(7)/(4)((3)/(4)m-(5)/(2))=(3)/(32)+(1)/(3)m`

We need to isolate
`m`:

`2m+(21)/(16)m-(35)/(8)=(3)/(32)+(1)/(3)m`

Grouping similar terms:

`2m+(21)/(16)m-(1)/(3)m=(3)/(32)+(35)/(8)`

`(143)/(48)m=(143)/(32)`

`m=(48)/(32)`

Dividing the numerator and the denominator by 16:

`m=(3)/(2)`