Solving linear equations

Task goals

• Solve a two-step equation such as $2x-5=11$ by undoing the operations in reverse order, showing the opposite operation performed at each step.
• Solve an equation with the variable on both sides, such as $2x-5=7x+12$, by collecting variable terms onto one side and constants onto the other before isolating the variable.
• Expand a bracket on one or both sides before collecting terms, such as $5(x-2)=3x+4$.
• Solve an equation with a fractional coefficient, such as $\tfrac{2}{3}x=8$, by multiplying both sides by the reciprocal so the coefficient of $x$ becomes $1$.
• Give an exact fraction answer, such as $x=\tfrac{7}{5}$, when a linear equation does not have a whole-number solution.
• Give an exact surd answer, such as $x=5-\sqrt{2}$ or $x=3\sqrt{2}$, when a linear equation has an irrational coefficient or constant.
• Verify a solution by substituting it back into the original equation, and identify a common error such as a missed sign or an unexpanded bracket.