Rearranging Formulas and Expanding Brackets

Vocabulary flashcards covering core concepts and step-by-step rearrangement methods from the video lecture.

Subject of an Equation

The single variable isolated on the left-hand side of a formula equal to the rest of the expression on the right-hand side.

Fraction Line for Division

A notation used in formula rearrangement to show division across an entire expression without needing brackets.

Expanding the Bracket in Rearranging

The process of multiplying an outside number by each term inside a bracket (such as multiplying $3$ by $2$ and $x$ to obtain $6 + 3x$) when isolating a target variable inside a bracket.

Rearranging $y - 4 = 3x$ for $x$

Dividing the whole expression $y - 4$ by $3$ using a fraction line to get $\frac{y - 4}{3} = x$, then swapping sides to arrive at $x = \frac{y - 4}{3}$.

Rearranging $a + 5 = \frac{b}{3}$ for $b$

Multiplying the left-hand side by $3$ to form $3(a + 5)$, expanding to $3a + 15 = b$, and writing $b = 3a + 15$.

Rearranging $2y = 3(2 + x)$ for $x$

Expanding the bracket to get $2y = 6 + 3x$, subtracting $6$ to get $2y - 6 = 3x$, dividing by $3$, and swapping sides to obtain $x = \frac{2y - 6}{3}$.

Rearranging $6a = \frac{b}{2} + 3$ for $b$

Subtracting $3$ to get $6a - 3 = \frac{b}{2}$, multiplying both sides by $2$ to get $2(6a - 3)$, and expanding to reach $b = 12a - 6$.