Title: 11. Rearranging algebraic formulae
Course: Demonstrating STACK (v4.3.7)

The equation \( c = ab \) can be described as the subject, \(c\), in terms of \(a\) and \(b\). It is also possible to obtain equivalent expressions of the from:

\(a\) in terms of \(b\) and \(c\).
\(b\) in terms of \(a\) and \(c\).

Identify these expressions:

\(a\) =

\(b\) =
Feedback: To rearrange the equation \(c = ab\) to make \(a\) the subject divide both sides of the equation by \(b\) to give: \[ a = \frac{c}{b}. \] To make \(b\) the subject just divide by \(a\): \[ b = \frac{c}{a}. \]

Rearrange \([value] = [value]\) and make \(t\) the subject of the formula.

\(t\) =
Feedback: To rearrange formulae perform operations to both sides of the formulae to obtain an equation with t as the subject. \[[value] = [value]. \] Add \(d\) to both sides: \[ [value] = [value]. \] Divide by \([value]\): \[ [value] = [value]. \] Now you have an equation for \(t\).

Rearrange \(a-bx = c+dx\) and make \(x\) the subject of the formula.

\(x\) =
Feedback: To rearrange formulae perform operations to both sides of the formulae to obtain an equation with x as the subject. \[a-bx = c+dx. \] Gather like terms (with x's on a sepearate side) \[ a-c = (b+d)x. \] Divide by \(b+d\): \[ [value] = x. \] Now you have an equation for \(x\).

Rearrange \([value] = [value]\) and make \(p\) the subject of the formula.

\(p\) =
Feedback: To rearrange formulae perform operations to both sides of the formulae to obtain an equation with p as the subject. \[ [value] = [value]. \] Firstly, gather the like terms. This involves factoring \(p\) out of \([value]\) to give: \[ [value] = [value]. \] Divide by \([value]\): \[ [value] = [value]. \] Now you have an equation for \(p\).

Rearrange \([value] = [value]\) and make \(a\) the subject of the formula.

\(a\) =
Feedback: To rearrange formulae perform operations to both sides of the formulae to obtain an equation with \(a\) as the subject. \[ [value] = [value]. \] The aim is to get \(a\) on the opposite side of the equation to the other constants/variables. In order to do this it is clear we must 'free' the \(a\) from the brackets. We do this by multiplying out \([value]\) which gives: \[ [value] = [value]. \] Subtract \([value]\) from both sides: \[ [value] = [value]. \] Divide by \([value]\): \[ [value] = [value]. \] You now have an equation for \(a\).

Rearrange the following: \[a = b+\frac{x}{c}\] Make \(x\) the subject of the formula.

\(x\) =
Feedback: To rearrange formulae perform operations to both sides of the formulae to obtain an equation with \(x\) as the subject. \[ [value] = [value]. \] Subtract b from both sides: \[ [value] = [value]. \] Multiply by \(c\): \[ [value] = [value]. \] Now you have an equation for \(x\).

Rearrange the following: \[\frac{x}{a} + \frac{x}{b} = 2. \] Leave \(x\) the subject of the formula.

\(x\) =
Feedback: To rearrange formulae perform operations to both sides of the formulae to obtain an equation with \(x\) as the subject. \[ \frac{x}{a} + \frac{x}{b} = 2. \] Multiply both sides by \([value]\): \[ [value] = [value]. \] Factorise: \[ [value] = [value]. \] Divide both sides by \([value]\): \[ [value] = [value]. \] Now you have an equation for \(x\).

Rearrange the following: \[a=[value].\] Make \(x\) the subject of the formula.

\(x\) =
Feedback: To rearrange formulae perform operations to both sides of the formula to obtain an equation with \(x\) as the subject. \[ a=[value]. \] To remove the surd, square both sides of the equation: \[ [value] = [value]. \] Divide by \([value]\): \[ [value] = [value]. \] Now you have an equation for \(x\).

Rearrange the following so that \(x\) is the subject of the formula: \[[value] = [value].\]
\(x\) =
Feedback: To rearrange formulae perform operations to both sides of the formula to obtain an equation with \(x\) as the subject. \[ [value] = [value]. \] To remove the surd, square both sides of the equation: \[ [value] = [value]. \] Subtract \(b\) from both sides: \[ [value] = [value]. \] Now you have an equation for \(x\).

Rearrange the following and make \(x\) the subject of the formula. \[ [value] = [value]. \] You may assume that \(x>0\) in this question.

\(x\) =
Feedback: To rearrange formulae perform operations to both sides of the formula to obtain an equation with \(x\) as the subject. \[ [value] = [value]. \] Subtract \([value]\) from both sides of the equation: \[ [value] = [value]. \] Multiply both sides by \([value]\): \[ [value] = [value]. \] Take square roots of both sides: \[ [value] = [value]. \] Now you have an equation for \(x\).

Rearrange the following and make \(x\) the subject of the formula. \[ [value] = [value]. \] You may assume that \(x>0\) in this question.

\(x\) =
Feedback: To rearrange formulae perform operations to both sides of the formula to obtain an equation with \(x\) as the subject. \[ [value] = [value]. \] First, square both sides of the equation to remove the square root: \[ [value] = [value]. \] Subtract 4 from both sides: \[ [value] = [value]. \] Take square roots of both sides: \[ [value] = [value]. \] Now you have an equation for \(x\).