Solution for [tex] \frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25 [/tex]
Further explanation
We add [tex] \frac{1}{7} [/tex] to both sides:
[tex] \frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7} [/tex]
Simplify:
[tex] \frac{2}{7}m = \frac{3}{14} + \frac{1}{7} [/tex]
On the right side for the addition operation, we equate the common denominator by multiplying [tex] \ \frac{1}{7} \ by \ \frac{2}{2} [/tex]
[tex] \frac{2}{7}m = \frac{3}{14} + \frac{2}{14} [/tex]
Then we combine terms to get:
[tex] \frac{2}{7}m = \frac{5}{14} [/tex]
Finally, we divide by the coefficient of m, or in other words, multiply both sides by [tex] \frac{7}{2} [/tex]:
[tex] \frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2} [/tex]
[tex] m = \frac{35}{28} [/tex]
We simplify fractions, both the numerator and denominator are divided equally by 7.
[tex] \boxed{ \ m = \frac{5}{4} \ } [/tex]
In the form of mixed fractions, we get:
[tex] \boxed{ \ m = 1 \frac{1}{4} \ }[/tex]
In decimal form, we get
[tex] m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }[/tex]
Check the solution into the equation:
[tex] \big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14} [/tex]
[tex] \frac{10}{28} - \frac{1}{7} = \frac{3}{14} [/tex]
[tex] \frac{5}{14} - \frac{2}{14} = \frac{3}{14} [/tex]
[tex] \frac{3}{14} = \frac{3}{14} [/tex]
Both sides show the same value, so the solution is correct.
Again, quick steps in summary:
[tex] \frac{2}{7}m - \frac{1}{7} = \frac{3}{14} [/tex]
[tex] \frac{2}{7}m = \frac{3}{14} + \frac{1}{7} [/tex]
[tex] \frac{2}{7}m = \frac{3}{14} + \frac{2}{14} [/tex]
[tex] \frac{2}{7}m = \frac{5}{14} [/tex]
[tex] m = \frac{5}{14} \times \frac{7}{2} [/tex]
[tex] m = \frac{35}{28} [/tex]
[tex] \rightarrow \boxed{ \ m = \frac{5}{4} \ } [/tex]
[tex] \rightarrow \boxed{ \ m = 1 \frac{1}{4} \ }[/tex]
[tex] \rightarrow \boxed{ \ m = 1.25 \ }[/tex]
Note:
This is a question about equations with one variable and we must calculate the value of the variable m. Our task is to isolate the variable m alone at the end of the process on one side of the equation, until the variable will be equal to a value on the opposite side.
The important thing to do is how to manipulate both sides of the equation with the algebraic properties of equality such as:
- adding,
- subtracting,
- multiplying, and/or
- dividing both sides of the equation with the same number.
All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation. In the form of fractions, the steps that must be considered are
- equate the denominator,
- simplify fractions, and
- turn fractions into mixed fractions or decimal forms.
It is very important to practice a lot until you get used to and know which operations should be done first.
Learn more
- A word problem that forms a single variable linear equation https://brainly.com/question/1566971
- Learn more about single variable linear equation that has no solution, has one solution, and has infinitely many solutions https://brainly.com/question/2595790
- Questioning the stages of solving a word problem about one variable linear equations https://brainly.com/question/2038876
Answer details
Grade : Middle School
Subject : Mathematics
Chapter : Linear Equation in One Variable
Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14, 5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, substract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal, brainly
