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Rearranging formulas

Algebraic expressions

Japanese school year: Junior high 2

What you learn

You will learn how to rearrange equations to solve for a specific variable using algebraic properties. This skill is frequently applied to transform geometric formulas and scientific equations to isolate desired quantities. Prior understanding of solving basic linear equations and transposing terms is helpful for this topic.

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Key points

This is the procedure to solve an equation for a specific variable. Move all terms containing the target variable to the left side and all other terms to the right side.

This basic algebraic step isolates the variable xx. Dividing both sides of the equation by the coefficient aa (a≠0a \neq 0) yields x=bax = \frac{b}{a}.

ax=b  ⟺  x=ba(a≠0)ax = b \iff x = \frac{b}{a} \quad (a \neq 0)

This describes how to handle equations with fractions. Multiply both sides by the common multiple of denominators to clear fractions, expand parentheses, and then rearrange.

This formula calculates the height hh when the area SS and base aa of a triangle are known. It is derived by rearranging the standard area formula for hh.

S=12ah  ⟺  h=2Sa(a≠0)S = \frac{1}{2}ah \iff h = \frac{2S}{a} \quad (a \neq 0)

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