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7. Linear Equations and Inequalities eLearn.Punjab
Sometimes it may happen that the solution(s) obtained do not satisfy Version: 1.1
the original equation. Such solution(s) (called extraneous) must be
rejected. Therefore, it is always advisable to check the solutions in the
original equation.
Example 3
Solve and check |3x + 10 | = 5x + 6
Solution
The given equation is equivalent to
± (3x + 10) = 5x + 6
i.e., 3x + 10 = 5x + 6 or 3x + 10 = –(5x+ 6)
–2x = –4 or 8x = –16
x = 2 or x = –2
On checking in the original equation we see that x = –2 does not
satisfy it. Hence the only solution is x = 2.
EXERCISE 7.2
1. Identify the following statements as True or False.
(i) | x | = 0 has only one solution. ……
(ii) All absolute value equations have two solutions. ……
(iii) The equation | x | = 2 is equivalent to x = 2 or x = –2. ……
(iv) The equation | x – 4 | = –4 has no solution. ……
(v) The equation | 2x – 3 | = 5 is equivalent to 2x – 3 = 5 or
2x + 3 = 5 . ……
2. Solve for x
(i) |3x - 5| = 4 (ii) 1 |3x + 2| - 4 = 11
2
(iii) |2x + 5| = 11 (iv) |3 + 2x| = |6x – 7|
(v) |x + 2| - 3 = 5 - |x + 2| (vi) 1 |x + 3| + 21 = 9
2
(vii) 3x - 5 - 1 =2 (viii) x + 5 = 6
2 33 2-x
11
