Could you show me how to do
5z/7 - 5z/8 = 1
The answer is 56/7
But how did they get it ?
sorry the correct answer is 56/5
40z/56 - 35z/56 = 1
5 z/56 = 1
z = 56/5
Thank you :)
To solve the equation 5z/7 - 5z/8 = 1, we need to combine the fractions on the left side and then isolate the variable z. Here's a step-by-step explanation of how to do it:
Step 1: Find a common denominator:
To combine the fractions, we need to find a common denominator for 7 and 8. In this case, the least common multiple of 7 and 8 is 56. So, we rewrite the equation with a common denominator:
(8 × 5z)/(8 × 7) - (7 × 5z)/(7 × 8) = 1
Step 2: Simplify the fractions:
We simplify the fractions by multiplying the numerators and the denominators:
(40z/56) - (35z/56) = 1
Step 3: Combine the fractions:
Now that we have the same denominator, we can subtract the fractions:
(40z - 35z)/56 = 1
Step 4: Simplify the expression:
Combine like terms on the numerator:
5z/56 = 1
Step 5: Solve for z:
To isolate z, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 56:
(5z/56) × 56 = 1 × 56
5z = 56
Step 6: Solve for z:
Finally, divide both sides by 5 to solve for z:
5z/5 = 56/5
z = 56/5
Step 7: Simplify the fraction:
To get the final answer in simplest form, we divide 56 by 5:
z = 11 1/5 or 56/5
So, the solution to the equation 5z/7 - 5z/8 = 1 is z = 56/5.