Question

3/5 (3-2z) = 2/5 (9-z)-0,3 (z-9) ​

Answer 1

3/5 (3-2z)=2/5 (9-z)-0,3 (z-9)
9/5-6/5z=18/5-2/5z-0,3z+2,7
9/5-6/5z=18/5-2/5z-0,3z+27/10
9/5-6/5z=63/10-2/5z-3/10z
18-12z=63-4z-3z
18-12z=63-7z
-12z+7z=63-18
-5z=45
z=-9

Answer 2

To solve the equation, let's simplify both sides step by step.

Starting with the left side of the equation: 3/5(3-2z) = (3/5)(3) - (3/5)(2z) = 9/5 - (6/5)z = (9 - 6z)/5

Moving on to the right side of the equation: 2/5(9-z) - 0.3(z-9) = (2/5)(9-z) - 0.3(z-9) = (18/5 - (2/5)z) - (0.3z - 2.7) = (18/5 - 2/5z) - 0.3z + 2.7 = 18/5 - 2/5z - 0.3z + 2.7 = 18/5 - (2/5 + 0.3)z + 2.7 = 18/5 - (2/5 + 3/10)z + 2.7 = 18/5 - (4/10 + 3/10)z + 2.7 = 18/5 - (7/10)z + 2.7 = (36/10 - 7/10z) + (27/10) = (36 - 7z + 27)/10 = (63 - 7z)/10

Now, the equation becomes: (9 - 6z)/5 = (63 - 7z)/10

To eliminate the fractions, we can multiply both sides of the equation by the common denominator, which is 10 in this case: 10 * (9 - 6z)/5 = 10 * (63 - 7z)/10

Canceling out the denominators: 2(9 - 6z) = 63 - 7z

Expanding the parentheses: 18 - 12z = 63 - 7z

Grouping like terms: -12z + 7z = 63 - 18

Combine like terms: -5z = 45

Dividing both sides by -5: z = -45/5 z = -9

Therefore, the solution to the equation is z = -9.