Question

Please show all working, thank you​

Answer 1

When we make the x the subject, we are "solving for x"

A. x = $\frac{1}{2}$y + 4$\frac{1}{2}$

Given:  y = 2x - 9

Add 9 to both sides (flipping the equation, but it is still equivalent): 2x = y + 9

Dividing both sides by 2: x = $\frac{1}{2}$y + 4$\frac{1}{2}$

B. x = 4y - 28

Given: y = $\frac{x}{4}$ + 7

Subtract 7 from both sides: y - 7 = $\frac{x}{4}$

Multiply both sides by 4 (flipping the equation, but it is still equivalent): x = 4y - 28

C. x = 2y - 6

Given: y = $\frac{x+6}{2}$

Multipy both sides by 2: 2y = x + 6

Subtract 6 from both sides of the equation (flipping the equation, but it is still equivalent): x = 2y - 6

D. x = $\frac{4}{3}$y

Given: y = $\frac{3x}{4}$

Multiply both sides by 4 (flipping the equation, but it is still equivalent): 3x = 4y

Divide both sides by 3: x = $\frac{4}{3}$y

E. x = $\sqrt{y - 11}$

Given: y = x² + 11

Subtract 11 from both sides: y - 11 = x²

Square root both sides (flipping the equation, but it is still equivalent): x = $\sqrt{y - 11}$

F. x = $\frac{y^{2}}{2}$y²

Given: y = $\sqrt{2x}$

Square both sides: y² = 2x

Flip the equation (still equal) and divide both sides by 2: x = $\frac{y^{2}}{2}$y²

Have a nice day! Sorry that this is long, there is a lot to say haha!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather