G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

 

Year 10 Interactive Maths - Second Edition


Adding a Number to Each Side of an Inequality

Adding a number to each side of an inequality does not change the sign of the inequality.

Example 23

Solve the inequality x - 4 >= 1 for x.

Solution:

Add 4 to each side to find x >= 5.  Therefore, the solution set is {x : x >= 5}.


Note:

(i)  The solution set consists of all numbers greater than or equal to 5, and is shown on the number line as follows:

The number line that represents numbers greater than or equal to 5. 
      The solid dot at 5 in this diagram means that 5 is an element of the solution set.

(ii)  {x : x >= 5} is read as 'the set of all numbers x such that x is greater than or equal to 5.

 

Study Another Topic in Chapter 2: Linear Equations and Inequalities

Solving Equations ] Equations Involving Two or More Operations ] Equations Containing Brackets ] Equations Containing Fractions ] Problem Solving ] Consecutive Numbers ] Solving Inequalities ] [ Adding a Number to Each Side of an Inequality ] Multiplying Each Side of an Inequality by a Positive Number ] Dividing Each Side of an Inequality by a Positive Number ] Multiplying Each Side of an Inequality by a Negative Number ] Dividing Each Side of an Inequality by a Negative Number ] Inequalities Involving Two Operations ] Inequalities Containing Brackets ] Inequalities Containing Fractions ] Transposition of Formulas ] Transpositions Involving Subtraction ] Transpositions Involving Division ] Transpositions Involving Multiplication ] Transpositions Involving Squares ] Transpositions Involving Square Roots ] Transpositions Involving Brackets ] Transpositions Involving Fractions ] Transpositions Involving Two or More Operations ] Subject Occurring Twice ] Substitution ] Problem Solving ] Problem Solving Unit ] Symbols ] Index ]

 

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