How do I solve z+9/2 + z-3/3=6
multiply both sides by six.
3(z+9)+2(z-3)=36
3z+27+2z-6=36
5z=36-21
solve for z.
z+9/2 + z-3/3=6
2z + 4 1/2 - 1 = 6
2z + 3 1/2 = 6
2z = 2 1/2
z = 1 1/4
Check it by substituting 1 1/4 for z in your original problem. Is that the correct answer?
To solve the equation z + 9/2 + z - 3/3 = 6, we need to simplify and isolate the variable z.
Step 1: Combine like terms
On the left side of the equation, we have z + z and 9/2 - 3/3.
z + z simplifies to 2z.
To combine 9/2 and -3/3, we need to find a common denominator. The common denominator between 2 and 3 is 6. Multiply the numerator and denominator of 9/2 by 3, and the numerator and denominator of -3/3 by 2:
(9/2) * 3 = 27/6
(-3/3) * 2 = -6/6
Now, the equation becomes:
2z + 27/6 - 6/6 = 6
Step 2: Combine the fractions
The fractions 27/6 and -6/6 have the same denominator of 6, so we can add them:
27/6 - 6/6 = 21/6
Now the equation is:
2z + 21/6 = 6
Step 3: Move constants to the other side of the equation
To isolate the variable z, we need to move the constant term 21/6 to the other side of the equation. We do this by subtracting it from both sides:
2z + 21/6 - 21/6 = 6 - 21/6
21/6 - 21/6 simplifies to zero, so we have:
2z = 6 - 21/6
Step 4: Simplify the right side of the equation
To simplify the right side, we need to find a common denominator between 6 and 21/6. The common denominator is 6. Multiply the numerator and denominator of 21/6 by 6:
(21/6) * 6 = 21
Now the equation becomes:
2z = 6 - 21
Step 5: Solve for z
To solve for z, subtract 21 from 6:
2z = -15
Finally, divide both sides of the equation by 2:
2z/2 = -15/2
The final solution is:
z = -15/2