Q# 1: Find the solution set of 3x+1<7 , and show on the number line.
Solution:
First understand the meaning of = For all values = belongs to W= whole numbers So it is basically saying the inequality is only for all values of x that belongs to whole numbers. So the solution set will have only whole numbers.
Now Write the Inequality
3x+1<7
Solve the constant
3x<7-1
3x<6
Divide by the coefficient of the variable
\frac{3x}{3} < \frac{6}{3}
x<2
Our solution will only contains whole numbers and the answer is suggesting that all values less than 2. Therefore, the solution set is and represented in number line as:
Q# 2: Find the solution set of -6<2x+1<11, \forall x\in Z and show on the number line.
Solution:
First understand the meaning of = For all values = belongs to Z= Integers So it is basically saying the inequality is only for all values of x that belongs to integers. So the solution set will have only integer numbers.
Now Write the Inequality
-6<2x+1<11
Since there are two inequalities, it can be expressed as
-6<2x+1 and 2x+1<11
Solve the constant
-6-1<2x and 2x<11-1
-7<2x and 2x<10
Divide by the coefficient of the variable
\frac{-7}{2}<\frac{2x}{2} and \frac{2x}{2}<\frac{10}{2}
\frac{-7}{2}<x and x<5
-3.5<x and x<5
Our solution will only contains integer numbers and the answer is suggesting that all values greater than -3.5 and less than 5. Therefore, the solution set is and represented in number line as:
