Lesson

Solving Equations

To solve an equation for $x$, isolate $x$ using inverse operations. Linear equations undo addition and multiplication; quadratics can be factorised or solved with the quadratic formula; exponential equations are undone with the natural logarithm.

Practice

Q1

Solve for $x$: $2x - 3 = 7$

Show hint

Undo the subtraction first.

Q2

Solve for $x$: $2x^2 - 3 = 7$

Show hint

Remember the negative root.

Now try the summary quiz. Factorise the quadratic, and take the natural logarithm to undo the exponential.

Quiz

Q1

Solve for $x$: $x^2 - 4x - 12 = 0$

Show hint

Find two numbers multiplying to $-12$ and summing to $-4$.

Q2

Solve for $x$: $e^x = 6$

Show hint

$\ln(e^x) = x$.