Coaching Centre
Harder equations and inequalities
Solving linear equations with several algebraic fractions, and solving linear inequalities with fractions, brackets and negative coefficients.
Several fractions
Solve $\dfrac{x - 2}{3} - \dfrac{x + 1}{4} = 1$.
Inequalities
Solve $-3(x - 2) < 12$.
Solve $\dfrac{x - 2}{3} - \dfrac{x + 1}{4} = 1$.
$x - 11 = 12$.
Solve $-3(x - 2) < 12$.
Divide by $-3$ and reverse.
Solve $\dfrac{2x - 3}{5} \ge 3$.
$2x - 3 \ge 15$.
Solve $4 - \dfrac{x}{2} \le 1$.
$-\tfrac{x}{2} \le -3$, reverse.
Solve $\dfrac{x + 3}{2} = \dfrac{x + 13}{4}$.
$2(x + 3) = x + 13$.
Solve $\dfrac{x}{2} + \dfrac{x}{3} = -5$.
$3x + 2x = -30$.
What is the smallest integer $x$ that satisfies $3x - 7 > 2(x - 1)$?
$3x - 7 > 2x - 2$, so $x > 5$.
Solve $\dfrac{3x}{4} - \dfrac{x}{2} = 1$.
$3x - 2x = 4$.
New numbers every time. Keep going until you get five in a row.