Inequalities

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1. 1Solving linear inequalitiesInequality signs and number lines, solving like an equation, turning the sign round for a negative, clearing fractions, double inequalities, the whole numbers in a range, and x in a denominator or a modulus.Done22 min
2. 2Inequalities on a graphShowing an inequality in x and y as a region: the boundary line, solid or dashed, testing a point to choose the side, several inequalities at once, reading inequalities from a graph, and quadratic inequalities.Done20 min

Past questions (70)

From 1984–2025: 26 WAEC, 2 NECO, 42 JAMB. Theory questions first, then objective, newest first.

Theory (20)

• WAEC 2023 · Paper 2 · Q7Aman spent $\frac13$ of his income on rent, $\frac16$ of the income in a fast food shop and $\frac34$ of the remaining amount was saved in a …
• WAEC 2020 · Paper 2 · Q4Shade the region, $P$, in the $x$–$y$ plane which satisfies simultaneously the inequalities: $$x + y \ge 5, \qquad 2y - x \ge 0, \qquad x + 5y …
• WAEC 2019 · Paper 2 · Q8Solve the inequality $\frac13x - \frac14(x + 2) \ge 3x - 1\frac13$.
• WAEC 2019 · Paper 2 · Q1Solve the inequality $\dfrac{1 + 4x}{2} - \dfrac{5 + 2x}{7} < x - 2$.
• WAEC 2018 · Paper 2 · Q8Lamin bought a book for ₦300.00 and sold it to Bola at a profit of $x\%$. Bola then sold the same book to James at a profit of $x\%$. If James …
• WAEC 2018 · Paper 2 · Q5Find the range of values of $x$ which satisfy the following inequalities simultaneously: $5 - x > 1$ and $9 + x \ge 8$.
• WAEC 2017 · Paper 2 · Q7Copy and complete the table of values for $y = 2x^2 - 7x - 9$ for $-3 \le x \le 6$.
• WAEC 2017 · Paper 2 · Q12If $\begin{pmatrix} 3x & 2 \\ 5 & 4 \end{pmatrix}\begin{pmatrix} 3 & -2 \\ 5 & 2y \end{pmatrix} = \begin{pmatrix} 28 & 4 \\ 35 & 22 \end{pmatrix}$, …
• WAEC 2016 · Paper 2 · Q3Given that $P = \{x : x \in \mathbb{R},\ 2x^2 - x - 10 \le 0\}$ and $Q = \{x : x \in \mathbb{R},\ 4x^2 - 1 \ge 0\}$, find $P \cap Q$.
• WAEC 2016 · Paper 2 · Q2Solve: $7(x + 4) - \frac23(x - 6) \le 2[x - 3(x + 5)]$.
• WAEC 2016 · Paper 2 · Q10Copy and complete the table of values for the relation $y = 2x^2 - 3x - 1$.
• WAEC 2016 · Paper 2 · Q4Solve the inequality $\frac23(1 - 4x) - \frac12(5 - 3x) \le \frac14(7 + 9x) - \frac13$.
• WAEC 2015 · Paper 2 · Q2Solve the inequality $4 + \frac34(x + 2) \le \frac38x + 1$.
• WAEC 2014 · Paper 2 · Q10(i) Solve the inequality $\frac12x - \frac56(x + 2) \le 1 + x$. (ii) Illustrate the solution on a number line.
• WAEC 2013 · Paper 2 · Q2Solve: $7x + 4 < \frac12(4x + 3)$.
• WAEC 2012 · Paper 2 · Q7(i) Using a scale of 2 cm to 1 unit on both axes, draw on the same graph sheet the graphs of $y - \frac{3x}{4} = 3$ and $y + 2x = 6$. (ii) From …
• WAEC 2010 · Paper 2 · Q2(i) Solve the inequality $\frac12x - \frac56(x + 2) \le 1 + x$. (ii) Illustrate the solution on a number line.
• WAEC 2009 · Paper 2 · Q11The polynomial $f(x) = 2x^3 + px^2 + qx + r$ is divisible by $(2x^2 - 7x + 3)$. It has a remainder of $-36$ when it is divided by $(x + 1)$. …
• WAEC 2009 · Paper 2 · Q2If $9\cos x - 7 = 1$ and $0^\circ \le x \le 90^\circ$, find $x$.
• WAEC 2008 · Paper 2 · Q8Copy and complete the table of values for the relation $y = -3x^2 + 12x$ for $-2 \le x \le 6$.

Objective (50)

• WAEC 2025 · Paper 1 · Q12Solve the inequality $\frac13(2x - 1) < 5$.
• WAEC 2025 · Paper 1 · Q19Which inequality is illustrated by the sketch graph? The boundary line passes through $(0, 3)$ and $(1, 0)$, and the region below the line is …
• WAEC 2024 · Paper 1 · Q29For what values of $x$ is $\dfrac{x - 3}{4} + \dfrac{x + 1}{8} \ge 2$?
• NECO 2023 · Paper 1 · Q24Which of the regions U, V, X, Y, Z shown satisfies the inequalities $0 < y < 2$, $y < 3 + x$, $x < 0$?
• NECO 2023 · Paper 1 · Q25Which of the following inequalities is represented by the number line shown?
• WAEC 2022 · Paper 1 · Q37Solve $\dfrac{y + 2}{4} - \dfrac{y - 1}{3} > 1$.
• WAEC 2021 · Paper 1 · Q43The distance $d$ between two villages is more than $18\text{ km}$ but not more than $23\text{ km}$. Which inequality represents the statement?
• WAEC 2020 · Paper 1 · Q13Solve $\frac13(5 - 3x) < \frac25(3 - 7x)$.
• JAMB 2017 · UTME · Q29Solve the inequality $x^2 + 2x > 15$.
• JAMB 2016 · UTME · Q13If $y = x^2 - x - 12$, find the range of values of $x$ for which $y \ge 0$.
• JAMB 2016 · UTME · Q22Solve the inequalities $-6 \le 4 - 2x < 5 - x$.
• JAMB 2016 · UTME · Q7Find the range of values of $x$ which satisfy the inequality $\left(\frac x2 + \frac x3 + \frac x4\right) < 1$.
• JAMB 2014 · UTME · Q17What is the solution of $\dfrac{x - 5}{x + 3} < -1$?
• JAMB 2014 · UTME · Q18Solve the inequality $\frac x2 + \frac34 \le \frac{5x}{6} - \frac{7}{12}$.
• JAMB 2013 · UTME · Q16Solve $3(x + 2) > 6(x + 3)$.
• JAMB 2013 · UTME · Q18Solve for $x$: $|x - 2| < 3$.
• JAMB 2012 · UTME · Q16The values of $y$ for which $\frac15y + \frac15 < \frac12y + \frac25$ are
• JAMB 2012 · UTME · Q17Find the range of values of $m$ which satisfy $(m - 3)(m - 4) < 0$.
• JAMB 2012 · UTME · Q18The shaded region is represented by the inequality
• JAMB 2011 · UTME · Q18Which of the following diagrams represents the solution of the inequalities $y \le x - 2$ and $y \ge x^2 - 4$?
• JAMB 2011 · UTME · Q19Solve the inequality $-6(x + 3) \le 4(x - 2)$.
• JAMB 2011 · UTME · Q20Solve the inequality $x^2 + 2x > 15$.
• JAMB 2010 · UTME · Q19For what range of values of $x$ is $\frac12x + \frac14 > \frac13x + \frac12$?
• JAMB 2010 · UTME · Q20Solve the inequalities $-6 \le 4 - 2x < 5 - x$.
• JAMB 2004 · UME · Q16The shaded area in the diagram is represented by
• JAMB 2004 · UME · Q17What are the integral values of $x$ which satisfy the inequality $-1 < 3 - 2x \le 5$?
• JAMB 2003 · UME · Q18Find the range of values of $x$ satisfying the inequalities $5 + x \le 8$ and $13 + x \ge 7$.
• JAMB 2003 · UME · Q20Triangle $OPQ$ in the graph is the solution of the inequalities
• JAMB 2002 · UME · Q37Use the graph to find the values of $p$ and $q$ if the shaded region is $px + qy < 4$.
• JAMB 2002 · UME · Q41Find the range of values of $x$ for which $\dfrac{x + 2}{4} - \dfrac{2x - 3}{3} < 4$.
• JAMB 2001 · UME · Q12Find the integral values of $x$ and $y$ satisfying the inequality $3y + 5x \le 15$, given that $y > 0$, $y < 3$ and $x > 0$.
• JAMB 2000 · UME · Q17Which of the graphs represents the solution of the simultaneous inequalities $2x - 2 \le y$ and $2y - 2 \le x$?
• JAMB 2000 · UME · Q21Solve the inequality $2 - x > x^2$.
• JAMB 1998 · UME · Q13Find the range of values of $m$ for which the roots of the equation $3x^2 - 3mx + (m^2 - m - 3) = 0$ are real.
• JAMB 1998 · UME · Q17If $x$ is a positive real number, find the range of values for which $\frac{1}{3x} + \frac12 > \frac{1}{4x}$.
• JAMB 1998 · UME · Q18The shaded area in the graph represents
• JAMB 1997 · UME · Q17Let $f(x) = 2x + 4$ and $g(x) = 6x + 7$, where $g(x) > 0$. Solve the inequality $\dfrac{f(x)}{g(x)} < 1$.
• JAMB 1997 · UME · Q18Find the range of values of $x$ which satisfies the inequality $12x^2 < x + 1$.
• JAMB 1995 · UME · Q16Solve the inequality $(x - 3)(x - 4) \le 0$.
• JAMB 1995 · UME · Q20Use the graph of the curve $y = f(x)$ to solve the inequality $f(x) > 0$.
• JAMB 1994 · UME · Q17Find the range of values of $x$ for which $\frac1x > 2$ is true.
• JAMB 1993 · UME · Q20Solve the inequality $y^2 - 3y > 18$.
• JAMB 1993 · UME · Q21If $x$ is negative, what is the range of values of $x$ within which $\frac{x + 1}{3} > \frac{1}{x + 3}$?
• JAMB 1992 · UME · Q16Find all values of $x$ satisfying the inequality $-11 \le 4 - 3x \le 28$.
• JAMB 1991 · UME · Q21Find the range of values of $x$ which satisfy the inequality $\frac x2 + \frac x3 + \frac x4 < 1$.
• JAMB 1989 · UME · Q25Find the range of values of $r$ which satisfies $\frac ra + \frac rb + \frac rc > 1$, where $a$, $b$ and $c$ are positive.
• JAMB 1987 · UME · Q26Solve the inequality $x - 1 > 4(x + 2)$.
• JAMB 1986 · UME · Q19Find all the numbers $x$ which satisfy the inequality $\frac13(x + 1) - 1 > \frac15(x + 4)$.
• JAMB 1984 · UME · Q19In a racing competition, Musa covered $5x$ km in the first hour and $(x + 10)$ km in the next hour. He was second to Ngozi, who covered a total …
• JAMB 1984 · UME · Q33Find the integral values of $x$ which satisfy the inequalities $-3 < 2 - 5x < 12$.