Solve the inequality 6x - 7 + x^2 > 0

Firstly rearrange the quadratic such that the coefficient of x2 is positive (already done in this example) and the quadratic is in the form of ax2 +bx + c, then solve for x, like you would solve a regular quadratic equation.
x2 + 6x - 7 > 0, (x + 7)(x - 1) > 0
This gives you the roots of this quadratic aka where the graph intersects the x axis. This is important as this tells you which values of x satisfy the inequality (would be best explained by drawing a quadratic graph). In this situation it is when the graph is above the x axis, so therefore be before the lowest root and after the highest root.
x = -7, x = +1
Therefore, x < -7, x > 1

Answered by Maths tutor

3035 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Evaluate the indefinite integral: ∫ (e^x)sin(x) dx


Find the exact solution to the equation: ln(3x-7) =5


Differentiate the following: y=sin(x^2+2)


The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences