Solving Inequalities (Edexcel IGCSE Maths): Exam Questions

Solve the inequality $x^{2}>3(x+6)$

$- 2 < n \text{less} - \text{than} or \text{slanted} \text{equal} to 3$

Represent this inequality on the number line.

Solve the inequality $8 x - 3 \text{greater} - \text{than} or \text{slanted} \text{equal} to 6 x + 4$

Solve $14n>11n+6$

On the number line below, show the set of values of $x$ for which $- 2 < x + 3 \text{less} - \text{than} or \text{slanted} \text{equal} to 4$

Solve $x^{2}>3x+4$

$- 5 < y \text{less} - \text{than} or \text{slanted} \text{equal} to 0$

$y$ is an integer.

Write down all the possible values of $y$.

Solve $6 ( x - 2 ) > 15$

$n$ is an integer.

$- 1 \text{less} - \text{than} or \text{slanted} \text{equal} to n < 4$ List the possible values of $n$.

Write down the inequality shown in the diagram.

Solve $y-2>5$

Solve $2x^{2}+3x-2>0$

$m$ is an integer such that $\text{long} \text{dash} 2 < m \text{less} - \text{than} or \text{slanted} \text{equal} to 3$

Write down all the possible values of $m$.

Solve $7x-9<3x+4$

$- 3 < n \text{less} - \text{than} or \text{slanted} \text{equal} to 1$

$n$ is an integer.

Write down all the possible values of $n$.

Solve the inequality $3p-7>11$

Solve the inequality $4x^{2}--5x--6>0$

Solve $6x+4>x+17$

$n$ is an integer with $\text{long} \text{dash} 5 < 2 n \text{less} - \text{than} or \text{slanted} \text{equal} to 6$

Write down all the values of $n$

Solve $3x-5<16$

Solve $x^{2}+2x>6x+5$

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

Write down the inequality shown on the number line.

Solve the inequality $4 y - 13 \text{less} - \text{than} or \text{slanted} \text{equal} to y + 8$

Show the inequality $x<3$ on the number line below

Solve the inequality $4 x - 7 \text{greater} - \text{than} or \text{slanted} \text{equal} to 13$

$n$ is an integer such that 3 n + 2 less-than or slanted equal to 14 and (6 n)/(n ^2 + 5) greater than 1

Find all the possible values of $n$.

On the number line, show the inequality $- 2 \text{less} - \text{than} or \text{slanted} \text{equal} to y < 1$

$n$ is an integer.

Write down all the values of $n$ that satisfy $- 3.4 < n \text{less} - \text{than} or \text{slanted} \text{equal} to 2$

Solve the inequality $6y+5>8$

Here is an inequality, in $x$, shown on a number line.

Write down the inequality.

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 $7t--8\leq2t+7$

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

$- 4 \text{less} - \text{than} or \text{slanted} \text{equal} to 2 y < 6$

$y$ is an integer.

Write down all the possible values of $y$.

Solve the inequality $5 y ^{2} - 17 y \text{less} - \text{than} or \text{slanted} \text{equal} to 40$

Solve the inequality $7 t - 3 \text{less} - \text{than} or \text{slanted} \text{equal} to 2 t + 31$ Show your working clearly.

Solve the inequalities $- 7 \text{less} - \text{than} or \text{slanted} \text{equal} to 2 x - 3 < 5$

On the number line, represent the solution set to part a).

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 $x.$

Solve the inequality $3x+15<8x+3$

Show clear algebraic working.

Solve the inequality 5 x minus 7 less-than or slanted equal to 2

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.

Solve the inequality $2 q \text{greater} - \text{than} or \text{slanted} \text{equal} to 31 - 3 q$

$n$ is an integer. Write down all the values of $n$ such that$- 2 \text{less} - \text{than} or \text{slanted} \text{equal} to n < 3$

On the number line, represent the inequality $y \text{less} - \text{than} or \text{slanted} \text{equal} to 1$

Here are two inequalities.

$- 2 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 3$ $9 \text{less} - \text{than} or \text{slanted} \text{equal} to x + y \text{less} - \text{than} or \text{slanted} \text{equal} to 11$

$x$ and $y$ are integers.

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

Solve.

$5x+1>x+13$

Solve $4>11-\frac{x}{3}$

Solve $5(x+3)<60$

Solve $x^{2}+2x>6x+5$

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

Martha’s solution to the inequality 8 x plus 5 less-than or slanted equal to 3 x minus 10 is shown on the number line.

Is her solution correct? Explain your reasoning.

$x$ is an integer.

$- 4 < x \text{less} - \text{than} or \text{slanted} \text{equal} to 2$

and

$2 \text{less} - \text{than} or \text{slanted} \text{equal} to x + 3 < 9$

Work out all the possible values of $x$.

Solve $--3x>6$

Solve the inequality 8 x minus 4 greater-than or slanted equal to 3 x minus 10

Solve the inequality.

$x ^{2} - 5 x - 6 \text{less} - \text{than} or \text{slanted} \text{equal} to 0$

Solve $8>3-\frac{1}{2}x$

Circle the inequality shown by the diagram.

Find the interval for which $x ^{2} - 7 x + 10 \text{less} - \text{than} or \text{slanted} \text{equal} to 0.$

.......................... $\text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to$ ..........................

Solve $7x+6>1+2x$

Here is a sketch of $y=f(x)$ where $f(x)$is a quadratic function. The graph intersects the $x$-axis where $x=--2.5$and $x=1$

Circle the solution of $f(x)>0$

Here is the graph of $y=f(x)$ where $f(x)$ is a quadratic function.

Write down all the integer solutions of $f ( x ) \text{greater} - \text{than} or \text{slanted} \text{equal} to 0$

Solve the inequality.

$3x-2>10$

Solve $5x+6\geq3x+15$

Write down the inequality represented by the number line.

Write down the largest integer that satisfies $5x-1<10.$

Solve the inequality $2 q \text{greater} - \text{than} or \text{slanted} \text{equal} to 31 - 3 q$

$- 2 \text{less} - \text{than} or \text{slanted} \text{equal} to n < 3$

$n$ is an integer

Write down all the possible values of $n$.

$m^{2}>9$

Circle the possible value of $m$.

Solve $3x+4<19$.

Show your solution on the number line.

Solve 3 x minus 5 greater-than or slanted equal to 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.