Changing the subject questions with answers

Questions

1. Question 1Linear formulas

   Make $x$ the subject of $y = 3x - 5$.

   Show the worked solution

   1. Step 1: Get the x term on its own$y + 5 = 3x$
   2. Step 2: Make x the subject$x = \dfrac{y + 5}{3}$
2. Question 2Divided by a number

   Make $x$ the subject of $y = \dfrac{2x + 1}{5}$.

   Show the worked solution

   1. Step 1: Clear the fraction$5y = 2x + 1$
   2. Step 2: Get the x term on its own$5y - 1 = 2x$
   3. Step 3: Make x the subject$x = \dfrac{5y - 1}{2}$
3. Question 3x in the denominator

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

   Show the worked solution

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

   Make $x$ the subject of $y = 5x^{2} - 3$.

   Show the worked solution

   1. Step 1: Get x² on its own$y + 3 = 5x^{2}$$x^{2} = \dfrac{y + 3}{5}$
   2. Step 2: Undo the square$x = \pm\sqrt{\dfrac{y + 3}{5}}$
5. Question 5Square roots

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

   Show the worked solution

   1. Step 1: Get √x on its own$y + 2 = 5\sqrt{x}$$\sqrt{x} = \dfrac{y + 2}{5}$
   2. Step 2: Undo the square root$x = \left(\dfrac{y + 2}{5}\right)^{2}$
6. Question 6x appears twice

   Make $x$ the subject of $y = \dfrac{3x + 7}{x - 4}$.

   Show the worked solution

   1. Step 1: Multiply both sides by the denominator$y(x - 4) = 3x + 7$
   2. Step 2: Expand the bracket$xy - 4y = 3x + 7$
   3. Step 3: Collect the x terms on one side$xy - 3x = 7 + 4y$
   4. Step 4: Factorise out x$x(y - 3) = 7 + 4y$
   5. Step 5: Divide both sides by the bracket$x = \dfrac{7 + 4y}{y - 3}$