Equations
Solving an equation means finding the number x that makes both sides equal. See every step — and the check that shows the answer is right.
The explanation is shown. Quick: linear and quadratic equations and formulas. Advanced: also inequalities — and a check with more numbers, so you can see why the answer fits.
Your numbers
3x + 4 = x + 10
Answer
x
3
How to work it out
- 13x + 4 = x + 10
- 22x + 4 = 10 (subtract 1x from both sides)
- 32x = 10 − 4 = 6 (subtract 4 from both sides)
- 4x = 6 / 2 = 3 (divide both sides by 2)
- 5Test: 13 = 13
The formula
Do the same on both sides
An equation is a balance scale: add, subtract, multiply or divide — but always on both sides.
d = b² − 4ac
The discriminant: d > 0 gives two solutions, d = 0 one, and d < 0 none.
x = (−b ± √d) / (2a)
−2x < 6 ⇔ x > −3
In an inequality: if you multiply or divide by a negative number, the sign flips.
U = R · I ⇔ I = U / R
Isolate a quantity: do the same on both sides until the one you want to find stands alone.
In depth: more numbers and “what if”
Try more numbers in the equation
| x | Left side | Right side | Equal? |
|---|---|---|---|
| 1 | 7 | 11 | No |
| 2 | 10 | 12 | No |
| 3 | 13 | 13 | Yes |
| 4 | 16 | 14 | No |
| 5 | 19 | 15 | No |
More: Equations and functions
- Formula with three quantitiesThe formula triangle: find the third quantity in A = B · C — e.g. U = R · I.
- FunctionsQuadratic function, inverse proportionality and power function — with a graph.
- Linear functiony = ax + b as a graph and table — the line through two points or the line of best fit.
- Scale and ratiosFrom drawing to reality, area and volume to scale, the rule of three and dividing in a ratio.
- Two equations with two unknownsSolve a system of equations step by step and see the intersection on the graph.
- Growth and decayPercentage growth, the growth rate from two measurements, and doubling time.