Answer: [tex]m=\frac{3}{2}[/tex]
Step-by-step explanation:
We have the following equation:
[tex]2m+\frac{7}{4}(\frac{3}{4}m-\frac{5}{2})=\frac{3}{32}+\frac{1}{3}m[/tex]
We need to isolate [tex]m[/tex]:
[tex]2m+\frac{21}{16}m-\frac{35}{8}=\frac{3}{32}+\frac{1}{3}m[/tex]
Grouping similar terms:
[tex]2m+\frac{21}{16}m-\frac{1}{3}m=\frac{3}{32}+\frac{35}{8}[/tex]
[tex]\frac{143}{48}m=\frac{143}{32}[/tex]
[tex]m=\frac{48}{32}[/tex]
Dividing the numerator and the denominator by 16:
[tex]m=\frac{3}{2}[/tex]
For this case we have the following equation:
[tex]2m + \frac {7} {4} (\frac {3} {4} m- \frac {5} {2}) = \frac {3} {32} + \frac {1} {3} m[/tex]
We apply distributive property on the left side of the equation:
[tex]2m + \frac {21} {16} m- \frac {35} {8} = \frac {3} {32} + \frac {1} {3} m[/tex]
We add similar terms from the left side:
[tex]\frac {53} {16} m- \frac {35} {8} = \frac {3} {32} + \frac {1} {3} m[/tex]
Add[tex]\frac {35} {8}[/tex]to both sides:
[tex]\frac {53} {16} m = \frac {3} {32} + \frac {1} {3} m + \frac {35} {8}[/tex]
We subtract [tex]\frac {1} {3} m[/tex] from both sides:
[tex]\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}[/tex]
We simplify:
[tex]143m=\frac{54912}{256}\\143m=\frac{13728}{64}\\143m=\frac{3432}{16}\\143m=\frac{858}{4}\\143m=\frac{429}{2}[/tex]
We divide between 143 on both sides:
[tex]m=\frac{429}{2*143}\\m=\frac{429}{286}\\m=\frac{33}{22}\\m=\frac{3}{2}[/tex]
ANswer:
[tex]m=\frac{3}{2}[/tex]
