 Hello and welcome to the session. In this session we will discuss the following question and the question says solve the in equation minus 4 is less than equal to 3x plus 5 is less than 17 and show the solution set on a number line. Write down the possible values of x if x is an integer. Let's start the solution now. We are given this in equation that is minus 4 is less than equal to 3x plus 5 is less than 17. This in equation can be split into two in equations. So this implies minus 4 is less than equal to 3x plus 5. This is the first in equation and 3x plus 5 is less than 17. This is the second in equation. Now we will solve them separately. First let us consider minus 4 is less than equal to 3x plus 5. Now we subtract 5 from both sides. So this implies minus 4 minus 5 is less than equal to 3x plus 5 minus 5. Since we have subtracted the same number from both the sides so the sign of inequality remains the same. This implies minus 9 is less than equal to 3x. Now we divide both sides by 3. So this implies minus 9 divided by 3 becomes minus 3 is less than equal to x. Or we can say that x is greater than equal to minus 3. So after solving the first in equation we get x is greater than equal to minus 3. Now we will solve the second in equation which is 3x plus 5 is less than 17. We will subtract 5 from both the sides so we get this implies 3x plus 5 minus 5 is less than 17 minus 5. This implies 3x is less than 12. Now we divide both sides by 3 so this implies x is less than 12 divided by 3 which is 4. So on solving the second in equation we get x is less than 4. So on combining the two solutions that we get we have minus 3 is less than equal to x is less than 4. We will now draw a number line to show this solution set. So we have drawn this number line and we will show minus 3 is less than equal to x is less than 4 on this number line. Now the portion to the right of minus 3 on the number line contains values which are greater than minus 3 and the portion to the left of 4 on the number line contains values which are less than 4. So this portion on the number line between minus 3 and 4 contains values which are greater than minus 3 and less than 4. Since minus 3 is included in the solution set so we will shape this circle at minus 3 since 4 is not included in the solution set so we make an open circle at 4. So the shaded portion of the number line represents the solution set and shaded circle at minus 3 means minus 3 is included in the circle means 4 is not included thus we have represented the solution set on the number line. Now we have to write down the possible values of x if x is an integer. Now if x is an integer then the possible values of x are now the solution set is minus 3 is less than equal to x is less than 4 and if x is an integer then all the integers which are greater than equal to minus 3 and less than 4 are minus 3 minus 2 minus 1 0 1 2 3. Now we will plot these values of x on the number line so we have drawn this number line now we will plot the points minus 3 minus 2 minus 1 0 1 2 3 on this number line. So if x is an integer then the solution set is minus 3 minus 2 minus 1 0 1 2 3 and we have plotted all these possible values of x from the solution set on the number line. With this we end our session hope you enjoyed the session.