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22 Nov 2010, 00:17
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E
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Which of the following inequalities is equivalent to 10 – 2x > 18?
(A) x > -14
(B) x > -4
(C) x > 4
(D) x < 4
(E) x < -4
(A) x > -14
(B) x > -4
(C) x > 4
(D) x < 4
(E) x < -4
Can someone clarify my doubt on inequality
1) when can we move elements from one side of inequality ( < or > ) to other side in the same way we do when we have = as a sign in place of inequality ?
2x+3y>9 , can we move 3y to the right side e.g. 2x>9-3y or not
2x*3y>9 , can we move x or y from left side to right side e.g 2*3>9/xy , or not , if not why
1) when can we move elements from one side of inequality ( < or > ) to other side in the same way we do when we have = as a sign in place of inequality ?
2x+3y>9 , can we move 3y to the right side e.g. 2x>9-3y or not
2x*3y>9 , can we move x or y from left side to right side e.g 2*3>9/xy , or not , if not why
22 Nov 2010, 06:01
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hirendhanak
You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.
To illustrate,
10 – 2x > 18
10 > 18 + 2x (Correct)
10 - 18 > 2x (Correct)
-8/2 > x (Correct. You are dividing by 2, which is positive so no changes)
-4 > x or x < -4 (Correct)
On the other hand,
10 – 2x > 18
-2x > 18 - 10 (Correct)
x > 8/(-2) (Incorrect. When you divide by -2, the sign of the inequality flips so x < 8/(-2))
So inequality differs from equation in that you cannot divide/multiply an inequality by x if you do not know the sign of x. If x is positive, the inequality remains the same. If x is negative, it flips.)
19 Jun 2017, 16:28
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hirendhanak
Another approach to test values of x and eliminate answer choices.
An easy one to start with is x = 0
Replace x with 0 to get: 10 – 2(0) > 18
Simplify to get: 10 > 18. Doesn't work.
So, x cannot equal 0.
Since answer choices B and D suggest that 0 is a possible value of x, we can ELIMINATE those answer choices
We're left with A, C and E
Now try x = 15
Replace x with 15 to get: 10 – 2(15) > 18
Simplify to get: -20 > 18. Doesn't work.
So, x cannot equal 15.
Since answer choices A and C suggest that 15 is a possible value of x, we can ELIMINATE those answer choices
By the process of elimination, we can conclude that the correct answer is E
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