z+7/8 = z+8/9

Question

Solve z+7  = z+8

          8          9

Answer 1

Mitze,

If the equation is (z+7)/8 = (z+8)/9 it does have a solution!

First we multiply each side by 9 to get

9(z+7)/8 = z+8 

then we multiply each side by 8 to get

9(z+7) = 8(z+8)

simplify

9z + 63 = 8z +64

subtract 8z form each side to get

z + 63 = 64 and finalyy subtract 63 from each side

z= 64-63=1

so z= 1

Plug it back in the original equation

(z+7)/8 = (z+8)/9

so

(1+7)/8 = (1+8)/9

and

8/8 = 9/9 = 1

so z=1

Hope that helps!

Art

Answer 2

(z+7)/8 = (z+8)/9

cross multiply (multiply the numerator of each fraction by the denominator of the other fraction)

(z+7)9 = (z+8)8

9z + 63 = 8z +64

z = 64-63 = 1

check the answer: plug 1 into the original equation

8(9) = 9(8)

IF the problem had been z+7/8 = z+8/9 there would be no solution or rather no real solution. There are two surreal solutions: z= infinity and z=-infinity

Answer 3

The only way this is equation is a true statement is if 7/8 and 8/9 are the same fraction and they are not.

Think about balancing in algebra: z = z, sure, but when you add one fraction to one side you need to add the same fraction to the other side.  Since you are not adding the same fraction to both sides, you are not keeping the balance, and the equation is no longer a true statement.  When a equation is not a true statement, then there is no solution.

Answer 4

Hello Mitze, 

The equation z + 7/8 = z + 8/9 has no solution. the simplest way to solve this problem is to plug in numbers and solve. Think about what the equation is saying. What number can I add two different numbers to and get the same value? None, therefore no solution exists.

If the equation is (z+7) / 8 = (z+8) / 9 then a solution does exist.

1. Write the equation:(z+7) / 8 = (z+8) / 9
2. Now went want to multiply the denominators by the opposite equations so we no longer have fractions:  9 * (z+7) = 8 * (z+8)
3. Now distribute: 9z + 63 = 8z + 64
4. Now get like terms on the same side of the equal sign: 9z - 8z = 64 - 63
5. And you are left with z = 1.

You can check your self by substituting 1 in place of z in the original equation and verifying that both sides of the equation are equal.

Hope that helps