Coaching Centre
Inequalities and rearranging formulas
Solving linear inequalities including reversing the sign, and changing the subject of a formula.
Inequalities
Solve $5 - 2x \le 11$.
Solve $\dfrac{3 - x}{2} > 4$.
Changing the subject
Treat the formula like an equation and undo operations until the new subject is alone.
Make $t$ the subject of $v = u + at$.
Solve $5 - 2x \le 11$.
Divide by $-2$ and reverse.
Solve $\dfrac{3 - x}{2} > 4$.
$-x > 5$.
Make $t$ the subject of $v = u + at$.
Subtract $u$, then divide by $a$.
Make $h$ the subject of $A = \tfrac{1}{2}bh$.
Multiply by $2$, divide by $b$.
Solve $3x + 7 > 1$.
$3x > -6$.
Make $x$ the subject of $y = 3x - 6$.
Add $6$, divide by $3$.
What is the largest integer that satisfies $4 - 3x \ge 16$?
$-3x \ge 12$, so $x \le -4$.
Make $r$ the subject of $A = \pi r^2$ (with $r > 0$).
Divide by $\pi$, then square root.
New numbers every time. Keep going until you get five in a row.