4x + 2 = 10 this statement is either true of false
If x = 1, then 4x + 2 = 10 is false because 4(1) + 2 is ≠ 10
If x = 2, then 4x + 2 = 10 is true because 4(2) + 2 = 10
7.
B. x – 4 < 3 this statement is either true or false If x =6, then x – 4 is true because 6 – 4 < 3 If x = 10 , then x – 4 is false because 6 – 4 is not < 3
When a number replaces a variable in an equation (or inequality) to result in a true statement, that number is a solution of the equation (or inequality). The set of all solutions for a given equation (or inequality) as called the solution set of the equation (or inequality).
8.
Solution Set of Simple Equations and Inequalities in One Variable by Inspection
To solve an equation of inequality means to find its solution set. There are three(3) ways to solve an equation or inequality by inspection
In this method, one guesses and substitutes values into an equation of inequality to see if a true statement will result.
10.
Consider the inequality x – 12 < 4 If x = 18, then 18 – 12 is not < 4 If x = 17, then 17 – 12 is not < 4 If x = 16, then 16 – 12 is not < 4 If x = 15, then 15 – 12 < 4 If x = 14, then 14 – 12 < 4
Inequality x - 12 < 4 is true for all values of x which are less than 16. Therefore, solution set of the given inequality is x < 16.
2. Graph the solution set x ≤ -1 on a number line.
x ≤ -1
-2 -1 0 1
The ray indicates that the solution set of x ≤ -1 consist of all the numbers less than or equal to -1. The solid circle of -1 indicates that -1 is included in the solution set.
2. Six years ago, Mrs. dela Rosa was 5 times as old as her daughter Leila.
How old is Leila now if her age is one-third of her mother’s present age?
Solution:
Step 1: Let x be Leila’s age now
3x is Mrs. dela Rosa’s age now
Step 2: x – 6 is Leila’s age 6 years ago
3x – 6 is Mrs. dela Rosa’s age 6 years ago
Step 3: 5(x – 6) = 3x – 6
Step 4: 5(x – 6) = 3x – 6
5x – 30 = 3x – 6
5x – 30 + 30 = 3x – 6 + 30
5x = 3x + 24
5x – 3x = 3x +24 – 3x
2x = 24
2x/2 = 24/ 2
X = 12 Leila’s age now
3x = 36 Mrs. dela Rosa’s age now
Step 5: Check: Thrice of Leila’s present age, 12, is Mrs. dela Rosa’s presnt age, 36. Six years ago, Mrs. dela Rosa was 36 – 6 = 30years old which was five times Leila’s age, 12 – 6 = 6.