Linear Equations and Inequalities in One Variable Linear

Linear Equations and Inequalities in One Variable ➋ • Linear Equations and Inequalities in One Variable

Linear equation in one variable • A linear equation in one variable, also called a first-degree equation in one variable, is one where there is only one variable, and the exponent of the variable is positive one (1). • Ex. ➋ • Linear Equations and Inequalities in One Variable

Solving an equation • To solve an equation means to find the value of the variable that will make the equation true. And the value that will make the equation true or will satisfy the equation is called the solution. • Illus. 9 is a solution of x – 5 = 4. ➋ • Linear Equations and Inequalities in One Variable

Properties of equality • Reflexive Property: a = a • Symmetric Property: a = b → b = a • Transitive Property: (a = b and b = c ) → a = c • Addition Property of Equality: a=b→a+c=b+c • Multiplication Property of Equality: a = b → ac = bc ➋ • Linear Equations and Inequalities in One Variable

• Ex. ➋ • Linear Equations and Inequalities in One Variable

Rational equations • Equations which contain fractions that have variables in the denominator are called rational equations. • Ex. ➋ • Linear Equations and Inequalities in One Variable

Literal equation • To solve a literal equation means to derive a formula for a certain unknown or variable from a given formula. • Ex. ➋ • Linear Equations and Inequalities in One Variable

Word problems • To solve a word problem in Algebra means to find the value of an unknown quantity that would satisfy the conditions stated in the problem. • Types of problems: – Number relation • Ex. Find the largest of four consecutive odd integers if their sum is one hundred twenty. ➋ • Linear Equations and Inequalities in One Variable

Word problems – Measurement • Ex. The perimeter of a rectangle is eighty-six inches. If the width of the rectangle is nineteen inches less than the length, find the dimensions of the rectangle. – Money • Ex. Joseph invested Php 1. 4 M in two banks, one giving 6% simple interest per annum and the other 7% simple interest. After a year, the combined interest from both banks is Php 93, 000. How much did he invest at 7%? ➋ • Linear Equations and Inequalities in One Variable

Word problems – Work • Ex. Bob can clean a classroom chalkboard in 30 seconds while Elmer can do the same job in 36 seconds. If they work together, how long will it take them to clean a chalkboard? – Mixture • Ex. I have two kinds of Angel candy. The Cherub candy sells at Php 576 per kilo; the Seraph candy sells at Php 355 per kilo. If I mix 3. 2 kilos of Cherub candies with 5. 3 kilos of Seraph candies, how much should I sell the mixed candies per kilo? ➋ • Linear Equations and Inequalities in One Variable

Inequalities • Inequalities are mathematical statements that use symbols, such as > , < , ≥ , and ≤. • Two types: – Absolute inequality, which is true for all values of the variable(s) • Illus. – Conditional inequality, which is true only for certain values of the variable(s) • Illus. ➋ • Linear Equations and Inequalities in One Variable

Solving an inequality • The solution to an inequality is a number or set of numbers that, when substituted for the variable, makes the inequality true. There are three ways of showing the solution set, namely, the graphical, interval, and setbuilder notations. ➋ • Linear Equations and Inequalities in One Variable

Ex. ➋ • Linear Equations and Inequalities in One Variable

Word problems • Ex. The circumference C of a circle with radius r is computed using the formula C = 2πr. Find the interval of values of the radius so that the circumference is between 12 ft and 18 ft, inclusive. • Ex. A certain pediatric medicine must be stored at a temperature between 5 o. C and 10 o. C. What is the equivalent temperature range on the Fahrenheit scale? ➋ • Linear Equations and Inequalities in One Variable