Question

2/7m-1/7=3/14

Please solve showing work

Answer 1

(2/7)m - (1/7) = 3/14
2m/7 =(3/14) + (1/7)
2m/7 = (3/14) + 2(1/7)
here we are multiplying 2 with 1/7 to make the denominator same for addition.
2m/7 = (3/14) +(2/14)
2m/7 = (3 + 2)/14
2m/7 = 5/14
2m = (5 *7)/14
2m = 35/14
2m = 5/2
m = 5/4
m = 1.25
So the value of "m" is 1.25

Answer 2

Solution for $\frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25$

Further explanation

It is a case about one variable linear quations and we have to solve the equation to get the variable m.

Our main goal 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 the value on the opposite side.

Let us add $\frac{1}{7}$ to both sides:

$\frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

On the right side for the addition operation, we equate the common denominator by multiplying $\ \frac{1}{7} \ by \ \frac{2}{2}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

Then we combine terms to get:

$\frac{2}{7}m = \frac{5}{14}$

We divide by the coefficient of m, or in other words, multiply both sides by $\frac{7}{2}$:

$\frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2}$

Finally, the solution is obtained as follows

$m = \frac{35}{28}$

We simplify fractions, both the numerator and denominator are divided equally by 7.

$\boxed{ \ m = \frac{5}{4} \ }$

In the form of mixed fractions, we get:

$\boxed{ \ m = 1 \frac{1}{4} \ }$

In decimal form, we get

$m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

Wanna check the solution into the equation?

$\big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14}$

$\frac{10}{28} - \frac{1}{7} = \frac{3}{14}$

$\frac{5}{14} - \frac{2}{14} = \frac{3}{14}$

$\frac{3}{14} = \frac{3}{14}$

Both sides show the same value, so the solution is correct.

These are quick steps in summary:

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

$\frac{2}{7}m = \frac{5}{14}$

$m = \frac{5}{14} \times \frac{7}{2}$

$m = \frac{35}{28}$

$\rightarrow \boxed{ \ m = \frac{5}{4} \ }$

$\rightarrow \boxed{ \ m = 1 \frac{1}{4} \ }$

$\rightarrow \boxed{ \ m = 1.25 \ }$

Note:

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.

In the form of fractions, the steps that must be considered are

• equate the denominator,
• simplify fractions, and
• for the final answer, convert fractions to mixed fractions or decimal forms

All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation.

Let's practice a lot until you get used to and know which operations should be done first.

Learn more

1. A word problem that forms a single variable linear equation https://brainly.com/question/1566971
2. Learn more about single variable linear equation that has no solution, has one solution, and has infinitely many solutions https://brainly.com/question/2595790  
3. 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