4.5 over z equals 5.4 over 1.2 plus z the answer is 6 how do i get there?

Answer 1

4.5/z = 5.4/1.2+z

Multiply all terms by 1.2+z to eradicate the RHS denominator:

4.5(1.2+z)/z = (5.4+4.5z)/z = 5.4

Multiply all terms by z to eradicate the LHS denominator:

5.4+4.5z = 5.4z

Collect like terms remembering that 4.5z is now -4.5z because it has moved over to the other side of the equation:

5.4 = 5.4z-4.5z

Factorising the RHS of the equation:

5.4 = z(5.4-4.5)

Divide both sides of the equation by (5.4-4.5) to find the value of z:

z = 6

Answer 2

To solve the equation 4.5/z = 5.4/1.2 + z for z, you can simplify the right side of the equation first. 5.4/1.2 can be simplified to 4.5. After simplifying, the equation becomes 4.5/z = 4.5 + z. To eliminate the fraction, multiply both sides of the equation by z. This yields 4.5 = 4.5z + z^2. Rearrange the equation to form a quadratic equation: z^2 + 4.5z - 4.5 = 0. Factor the quadratic equation to obtain (z-1)(z+4.5) = 0. From here, you can see that z = 1 or z = -4.5. However, since the original equation had a positive value for z, the answer is z = 1.