Inequalities (Single) - 4 Types Of Recurring Questions

In this course, we will cover 4 commonly tested recurring question types involving inequalities with a single inequality sign. Each question type focuses on a different technique used when solving inequality equations. Through clear explanations and step-by-step examples, students will learn the methods required to solve these inequalities accurately and present their answers correctly.

Type 1: Combine Two Inequalities

Draw a number line to illustrate the inequalities \(x>-3\) and \(x\le3\) on a single number line.

Type 2: Divide/Multiple Negative Algebra

Solve the inequality \(3x-11>5x-8\).

Type 3: Fractional Inequalities

Solve the inequality \(\frac{1}{5}x-\frac{2}{3}x>-7\).

Hence, find the largest possible value of \(x\) if \(x\) is a prime number.

Type 4: Word Problem Sum

A fruit stall spends $12 to buy a carton of 150 mangoes.

  1. If the stall sells a mango for 50 cents, what is the profit the stall makes for each mango? Give your answer in cents.
  2. By forming an inequality, find the smallest number of mangoes that she can sell in order to make a total profit of more than $40.
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