Algebra Study Guide

Changing the subject means rearranging a formula so a chosen variable is isolated. Apply inverse operations to both sides and work in the reverse order from the operations acting on the new subject. Keep equations balanced and use brackets when an entire expression is divided.

From y = 3x + 5, subtract 5 and divide by 3 to get x = (y − 5)/3. From A = (a + b)h/2, multiply by 2, divide by h, then subtract a to obtain b = 2A/h − a. A final substitution can check the rearrangement.

A strong solution states the relevant rule, substitutes or transforms values carefully, shows intermediate reasoning, and checks that the result is reasonable and in the required form. Common errors come from omitted terms, mishandled signs, premature rounding or using a rule that does not match the structure of the problem.

Changing the subject of a formula means rearranging an equation so that a different variable is isolated on one side, typically the left-hand side. The subject is the single variable that the formula expresses in terms of all the other variables. For example, in the formula for the area of a rectangle, A = lw, 'A' is the subject because it's isolated. If you wanted to find the width 'w' given the area and length, you would need to rearrange the formula to make 'w' the subject. This process involves using inverse operations to move terms around the equals sign, much like solving a linear equation. Whatever operation you perform on one side of the equation, you must perform the exact same operation on the other side to maintain equality. These operations include addition/subtraction, multiplication/division, and sometimes more complex operations like squaring or taking square roots, though foundation level generally focuses on linear manipulations. The goal is always to get the desired variable by itself, with a coefficient of +1. Remember to work 'backwards' through the order of operations (BIDMAS/PEMDAS) when isolating the variable. For instance, deal with addition/subtraction terms first, then multiplication/division.