Solving Inequalities (AQA GCSE Maths: Higher): Exam Questions

$-2<n⩽3$

Represent this inequality on the number line.

Solve the inequality $8x-3⩾6x+4$

$-5<y⩽0$

$y$ is an integer.

Write down all the possible values of $y$.

Solve    $6\left(x-2\right)>15$

$m$ is an integer such that  $—2<m⩽3$

Write down all the possible values of $m$.

Solve   $7x-9<3x+4$

Solve $6x+4>x+17$

$n$ is an integer with $—5<2n⩽6$

Write down all the values of $n$

$m^2>9$

Circle the possible value of $m$.

Solve  $8>3-\frac{1}{2}x$

$x$ is an integer.

$–4<x⩽2$

and

$2⩽x+3<9$

Work out all the possible values of $x$.

Solve $7x+6>1+2x$

Solve  $5x+6>3x+15$

Write down the inequality represented by the number line.

Solve  $4>11-\frac{x}{3}$

Here is the graph of $y=\mathrm{f}\left(x\right)$ where $\mathrm{f}\left(x\right)$ is a quadratic function.

Write down all the integer solutions of $f\left(x\right)⩾0$

Write down the inequality shown on the number line.

Solve the inequality $4y-13⩽y+8$

On the number line, show the inequality $–2⩽y<1$

$n$ is an integer.

Write down all the values of $n$ that satisfy $–3.4<n⩽2$

Solve the inequality $7t–8\le 2t+7$

On the number line below, represent the solution set of the inequality solved in part (a).

Solve the inequality $7t–3⩽2t+31$

Show your working clearly.

Solve the inequality $3x+15<8x+3$

Show clear algebraic working.

Solve the inequality $2q⩾31–3q$

Solve  $3x+4<19$.

Show your solution on the number line.

Solve $3x-5⩾10$

Show your solution on the number line.

Gemma’s solution to the inequality $3x+1>-5$

Is Gemma’s solution correct?
Explain your reasoning.

Solve.

   $5x+1>x+13$

Solve $7-5x<-3$

Solve the inequality $x^2>3(x+6)$

Solve   $x^2>3x+4$

Solve   $2x^2+3x-2>0$

Here are two inequalities.

$–2⩽x⩽3$
$9⩽x+y⩽11$

$x$ and $y$ are integers.

Work out the greatest possible value of $y–x$

Here is a sketch of the curve    $y=x^2+4x-12$

Work out the values of $x$ for which    $x^2+4x–12<0$

Give your answer as an inequality.

$n$ is an integer such that $3n+2⩽14\mathrm{and}\frac{6n}{n^2+5}>1$

Find all the possible values of $n$.

Solve the inequality $4x^2–5x–6>0$

Solve $x^2+2x>6x+5$

Represent your solution set to part (a) on the number line below.

Here is a rectangle.

Given that the area of the rectangle is less than $75{\mathrm{cm}}^2$

find the range of possible values of $x$.

Solve the inequality $5y^2-17y⩽40$

The diagram shows a rectangle.

The area of the rectangle is $A{\mathrm{cm}}^2$
Given that $A<3x+27$
find the range of possible values for $x.$

Martha’s solution to the inequality $8x+5⩽3x-10$ is shown on the number line.

Is her solution correct?
Explain your reasoning.

Solve the inequality.

   $x^2-5x-6⩽0$

Find the interval for which $x^2-7x+10⩽0.$

.......................... $⩽x⩽$ ..........................