Changing the subject questions with answers

Questions

1. Question 1Linear formulas

   Make $x$ the subject of $y = 6x - 2$.

   Show the worked solution

   1. Step 1: Get the x term on its own$y + 2 = 6x$
   2. Step 2: Make x the subject$x = \dfrac{y + 2}{6}$
2. Question 2Divided by a number

   Make $x$ the subject of $y = \dfrac{3x - 1}{4}$.

   Show the worked solution

   1. Step 1: Clear the fraction$4y = 3x - 1$
   2. Step 2: Get the x term on its own$4y + 1 = 3x$
   3. Step 3: Make x the subject$x = \dfrac{4y + 1}{3}$
3. Question 3x in the denominator

   Make $x$ the subject of $y = \dfrac{-4}{x} - 4$.

   Show the worked solution

   1. Step 1: Get the fraction on its own$y + 4 = \dfrac{-4}{x}$
   2. Step 2: Clear the fraction$x(y + 4) = -4$
   3. Step 3: Make x the subject$x = \dfrac{-4}{y + 4}$
4. Question 4Squares (two answers)

   Make $x$ the subject of $y = 2x^{2} - 5$.

   Show the worked solution

   1. Step 1: Get x² on its own$y + 5 = 2x^{2}$$x^{2} = \dfrac{y + 5}{2}$
   2. Step 2: Undo the square$x = \pm\sqrt{\dfrac{y + 5}{2}}$
5. Question 5Square roots

   Make $x$ the subject of $y = 3\sqrt{x} - 9$.

   Show the worked solution

   1. Step 1: Get √x on its own$y + 9 = 3\sqrt{x}$$\sqrt{x} = \dfrac{y + 9}{3}$
   2. Step 2: Undo the square root$x = \left(\dfrac{y + 9}{3}\right)^{2}$
6. Question 6x appears twice

   Make $x$ the subject of $y = \dfrac{5x - 4}{x + 2}$.

   Show the worked solution

   1. Step 1: Multiply both sides by the denominator$y(x + 2) = 5x - 4$
   2. Step 2: Expand the bracket$xy + 2y = 5x - 4$
   3. Step 3: Collect the x terms on one side$xy - 5x = -4 - 2y$
   4. Step 4: Factorise out x$x(y - 5) = -4 - 2y$
   5. Step 5: Divide both sides by the bracket$x = \dfrac{-4 - 2y}{y - 5}$