Unit 2 · Core unit
Solving by undoing operations while keeping both sides balanced, and the one place inequalities behave differently from equations.
What a strong answer looks like
A strong answer states what was done to both sides at each step, and checks the solution back in the original.
Know
Solving reverses the operations applied to the variable, in the opposite order to how they were applied.
Apply
Clear brackets and fractions first, then collect the variable on one side.
Watch out
Applying an operation to only one side, or to only part of a side.
Study move
Solve an equation with brackets on both sides and substitute the answer back.
Know
Rearranging for one variable in terms of others uses the same moves as solving, but the answer is an expression rather than a number.
Apply
Treat every other letter as a fixed quantity and isolate the target.
Watch out
Dividing by a variable without noting it cannot be zero.
Study move
Rearrange a formula for each of its variables in turn.
Know
Inequalities solve like equations except that multiplying or dividing by a negative reverses the direction. And gives an intersection; or gives a union.
Apply
Solve as normal, flipping the sign only at a negative multiplication or division.
Watch out
Forgetting to reverse the inequality, which produces exactly the wrong half of the number line.
Study move
Solve an inequality requiring a flip, and graph the solution.
Modeling drill
Rearrange a cost formula to solve for the quantity, state any restriction, then use it to answer a question in context.
