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

3178 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the exact value of sin(75°). Give your answer in its simplest form.


Integrate 1/x


A particle of mass M is being suspended by two ropes from a horizontal ceiling. Rope A has a tension of 15N at 30 deg and rope B has a tension of xN at 45 deg, find M assuming the particle remains stationary.


Integrate (x)(e^x) with respect to x and then integrate (x)(e^x) with respect to y.


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning