Linear equations and ax² = c

Solving linear equations with brackets, pronumerals on both sides and algebraic fractions, and solving quadratic equations of the form ax² = c.

Harder linear equations

Example 1●●

Solve $5(x - 2) = 3(x + 4)$.

$5x - 10 = 3x + 12$

$2x = 22$, so $x = 11$

Example 2●●●

Solve $\dfrac{2x - 1}{3} = \dfrac{x + 4}{2}$.

$2(2x - 1) = 3(x + 4)$

Multiply both sides by 6

$4x - 2 = 3x + 12$, so $x = 14$

Example 3●●●

Solve $\dfrac{x}{3} + \dfrac{x}{4} = 7$.

$4x + 3x = 84$

Multiply every term by 12

$7x = 84$, so $x = 12$

Example 4●●

Solve $3x^2 = 48$.

$x^2 = 16$

$x = \pm 4$

Flashcards

Fractions on both sides

Multiply by the lowest common denominator.

$x^2 = 16$

$x = \pm 4$

$x^2 = -16$

No real solutions

Practice