Solve the inequality x^2 – x < 6
The question is asking for the range of x values that satisfies the inequality. First rearrange the equation to form a quadratic: x2 – x – 6 < 0. Factorise the quadratic to find x-intercepts: ( x – 3 )( x + 2) < 0. x-intercepts: x = 3 and x = -2. Sketch the quadratic using the intercepts. The inequality is asking for where the quadratic is less than 0. So the range of x values where the graph is below the x-axis satisfies the inequality. The range of x is -2 < x < 3
