8w + 5/10w -7 = 4w -3/5w +7
compare your post with that of
Giselle at
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Your equation has the same problem of interpretation.
To solve the equation 8w + 5/10w -7 = 4w -3/5w +7, we will first simplify both sides of the equation:
8w + (5/10w) - 7 = 4w - (3/5w) + 7
We can simplify the fractions by finding a common denominator. The common denominator for 10w and 5w is 10w, so we will multiply the first fraction by 1/2 and the second fraction by 2/2:
8w + (5/10w) - 7 = 4w - (3/5w) + 7
8w + (5/10w) - 7 = 4w - (6/10w) + 7
Now, let's combine like terms on both sides:
8w + 5/10w - 7 = 4w - 6/10w + 7
To simplify even further, we need to have the same denominator for both fractions:
8w + (5/10w) - 7 = 4w - (6/10w) + 7
Since the fractions already have the same denominator of 10w, we can combine them directly:
8w + 5/10w - 7 = 4w - 6/10w + 7
Now, we can simplify even further by combining like terms:
8w + (5/10w) - 7 = 4w - (6/10w) + 7
Simplifying the fractions:
8w + 1/2w - 7 = 4w - 3/5w + 7
Next, let's simplify further by combining like terms:
(8w + 1/2w) - 7 = (4w - 3/5w) + 7
Combining the terms:
8.5w - 7 = (20w - 3w)/5 + 7
Applying the distributive property:
8.5w - 7 = (17w/5) + 7
To get rid of the fraction, let's multiply both sides of the equation by 5:
5(8.5w - 7) = 5(17w/5) + 5(7)
Performing the multiplication:
42.5w - 35 = 17w + 35
Now, let's simplify further by combining like terms:
42.5w - 35 = 17w + 35
To isolate the variable w, let's move the 17w to the left side of the equation by subtracting 17w from both sides:
42.5w - 17w - 35 = 17w - 17w + 35
Simplifying:
25.5w - 35 = 35
Next, let's move the constant term (-35) to the right side of the equation by adding 35 to both sides:
25.5w - 35 + 35 = 35 + 35
Simplifying:
25.5w = 70
Finally, to solve for w, we divide both sides of the equation by 25.5:
(25.5w)/25.5 = 70/25.5
Simplifying:
w = 2.745
Therefore, the solution to the equation is w = 2.745.
To solve this equation for w, we will simplify both sides of the equation, combine like terms, and isolate the variable w.
Starting with the left side of the equation:
8w + 5/10w - 7
Step 1: Combine terms containing w
To add or subtract terms with w, they must have the same denominator. In this case, the denominator of 5/10w is 10. We can rewrite the equation as:
8w + (5/10w) - 7
Step 2: Simplify the fraction
The 5/10 fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5. This gives us:
8w + (1/2w) - 7
Moving on to the right side of the equation:
4w - 3/5w + 7
Step 3: Combine terms containing w
Again, to combine terms with w, we need a common denominator. The denominator of 3/5w is 5. This equation becomes:
4w - (3/5w) + 7
Now, we can rewrite the original equation as:
8w + (1/2w) - 7 = 4w - (3/5w) + 7
Step 4: Combine like terms
Combine the terms with w on each side of the equation:
(8w + 1/2w) - 7 = (4w - 3/5w) + 7
To combine 8w with 1/2w, you will need a common denominator, which is 2. Thus:
(16w/2 + 1/2w) - 7 = (20w/5 - 3/5w) + 7
Simplifying further:
16w/2 + 1/2w - 7 = 20w/5 - 3/5w + 7
Step 5: Use the distributive property to simplify
Multiply the numerators with the denominators:
(16w + w)/2 - 7 = (20w - 3w)/5 + 7
Combine the terms on each side of the equation:
(17w)/2 - 7 = (17w)/5 + 7
Step 6: Get rid of the fractions
To eliminate the fractions, we will multiply everything by the least common denominator (LCD), which is 10:
10[(17w)/2 - 7] = 10[(17w)/5 + 7]
This gives us:
10 * (17w/2) - 10 * 7 = 10 * (17w/5) + 10 * 7
Simplifying:
85w - 70 = 34w + 70
Step 7: Isolate the variable
Now, let's isolate the variable w by moving the terms with w to one side and the constant terms to the other side:
85w - 34w = 70 + 70
Combine like terms:
51w = 140
Step 8: Solve for w
Divide both sides by 51 to solve for w:
w = 140/51
The final solution to the equation is w = 2.7451 (rounded to four decimal places).