Advertisements
Advertisements
Question
Solve `2/3` (x + 1) + 4 < 10 and represent its solution on a number line.
Given replacement set is {-8, -6, -4, 3, 6, 8, 12}.
Advertisements
Solution
`2/3` (x + 1) + 4 < 10
`=> 2/3 ("x" - 1) < 10 - 4`
`=> 2/3 ("x" - 1) < 6`
⇒ 2(x − 1) < 18
⇒ x − 1 < 9
⇒ x − 1 + 1 < 9 + 1 ...(Adding 1 to both sides)
⇒ x < 10
Thus x < 10
Since, replacement set = {−8, −6, −4, 3, 6, 8, 12}
⇒ Solution set = {−8, −6, −4, 3, 6, 8}
APPEARS IN
RELATED QUESTIONS
Solve and graph the solution set on a number line: 7 > 3x – 8 ; x ∈ W
Solve and graph the solution set on a number line: 8x – 8 ≤ – 24 ; x ∈ Z
Fill in the blank, using the following number line:
An integer, on the given number line, is greater than every number to its_______
Fill in the blanks, using the following number line:
2 is _______ than – 4 implies 2 is to the ________ of – 4.
Fill in the blanks, using the following number line:
5 is _______ than 2 and -5 is ______ than – 2.
Fill in the blanks, using the following number line:
-6 is ______ than 3 and the opposite of -6 is ______than opposite of 3.
In the following case, arrange the given integers in ascending order using a number line.
3, – 3, 4, – 7, 0, – 6, 2
For the statement, given below, state whether it is true or false:
0 is greater than every positive integer.
In the following pairs of numbers, a state in which the whole number is on the left of the other number is on the number line. Also write it with the appropriate sign (>, <) between them.
370, 307
In the following pair of number, a state in which the whole number is on the left of the other number is on the number line. Also write it with the appropriate sign (>, <) between them.
98765, 56789
