I cant seem to understand this..
(w/21)-(w/49)=(1/21)
solve for w?
hint: multiply each term by (3x49) or 147
We have a fractional equation. Your first goal should be to do away with the fractions. It is easier to work with equations that have no fractions.
What is the LCD of 21 and 49?
Reiny said 147.
147/21 = 7
147/49 = 3
Yes, 147 = LCD.
We multiply each term on BOTH sides of the equation by the LCD.
(w/21)(147) = 7w
-(w/49)(147) = -3x
(1/21)(147) = 7
We now have a linear (not fractional) equation:
7w - 3w = 7
4w = 7
w = 7/4....This is our answer or is it?
How do we know that w = 7/4? We plug 7/4 in the original fractional equation and simplify.
You were given:
(w/21)-(w/49)=(1/21)
Our goal: To get 1/21 on BOTH sides of the fractional equation.
7/4 divided by 21 - 7/4 divided by 49 = 1/21
1/12 - 1/28 = 1/21
1/21 = 1/21...IT checks!!!
This means that the answer is w = 7/4.
Done!
To solve the equation (w/21) - (w/49) = (1/21) for w, you need to get rid of the fractions first. Here's how you can do it step by step:
Step 1: Find a common denominator for the fractions involved.
In this case, the least common multiple of 21 and 49 is 147.
Step 2: Rewrite each fraction with the common denominator.
(w/21) - (w/49) = (1/21) can be rewritten as:
(49w/147) - (21w/147) = 1/21
Step 3: Combine the fractions.
Now that the fractions have the same denominator, you can simplify the equation by subtracting the fractions.
(49w - 21w)/147 = 1/21
Step 4: Simplify the equation.
28w/147 = 1/21
Step 5: Cross-multiply and solve for w.
Multiply both sides of the equation by 21 to eliminate the fraction on the right side:
21 * (28w/147) = 21 * (1/21)
28w/7 = 1
Multiply both sides of the equation by 7 to eliminate the fraction on the left side:
7 * (28w/7) = 7 * 1
28w = 7
Step 6: Solve for w.
Divide both sides of the equation by 28 to isolate w:
28w/28 = 7/28
w = 1/4
So the solution for w is 1/4.