Swap the letter for its number, in brackets, then BEDMAS

A variable is a letter that stands for a number. In 3x + 2 the letter x can be any number. A number written right beside a letter means multiply: 3x means 3 × x, and 2(y + z) means 2 × (y + z). To substitute is to replace each letter with its number. To evaluate is to then work out the answer.

The golden rule: every time you put a number in for a letter, put it in brackets. If x = −5, then 3x becomes 3(−5) = −15 and x² becomes (−5)² = 25. The brackets keep the negative sign attached to its number, so nothing gets lost.

After the numbers are in, follow BEDMAS: Brackets, Exponents, Division and Multiplication left to right, Addition and Subtraction left to right. Evaluate 3z² − x when z = 2 and x = −5: write 3(2)² − (−5). Exponent first: (2)² = 4. Multiply: 3 × 4 = 12. Subtracting a negative is adding: 12 + 5 = 17.

A fraction bar or a division sign between brackets works like brackets too: finish the top and the bottom before you divide. (m + n) ÷ (m − n) with m = 4 and n = 6 is (4 + 6) ÷ (4 − 6) = 10 ÷ (−2) = −5.

A table of values is the same expression with several inputs. For 2x − 3: x = 1 gives 2(1) − 3 = −1, x = 0 gives −3, x = −1 gives −5, x = −2 gives −7. Notice each output drops by 2 when x drops by 1: the coefficient 2 is the step.

With brackets in the expression you have two roads, and both arrive at the same answer. 4(3x − 2y) with x = 3 and y = −4: distribute first to get 12x − 8y = 12(3) − 8(−4) = 36 + 32 = 68, or substitute first to get 4(9 + 8) = 4(17) = 68.