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Which of the following inequalities is equivalent to 10 – 2x > 18?

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Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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21 Nov 2010, 23:17
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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

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
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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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22 Nov 2010, 05:01
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hirendhanak wrote:
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

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

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.)
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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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19 Jun 2017, 12:50
[quote="hirendhanak"]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

Fastest way to solve this question is to quickly check the inequality sign of the answer choices.

Post a quick glance you notice two things.

1. all the values of the answer choices are positive
2. 3 answer choices have same sign and two have different signs

As you might know that the question has (-2) as the coefficient of "x" which means we need to multiply x by negative 2.

Only option E when multiplied with -2 and adding 10 will give us the answer.

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Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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19 Jun 2017, 15:28
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hirendhanak wrote:
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

Another approach to test values of x and eliminate answer choices.

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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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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19 Jun 2017, 21:01
hirendhanak wrote:
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

$$10 – 2x > 18$$

Or, -8 > 2x

Or, 2x < - 8

Or, x < -4

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Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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20 Jun 2017, 08:16
Since 10 – 2x > 18 is the inequality statement my answer would be (B) x > -4.
Any value greater than -4 will satisfy the inequality equation.

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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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20 Jun 2017, 08:21
FB2017 wrote:
Since 10 – 2x > 18 is the inequality statement my answer would be (B) x > -4.
Any value greater than -4 will satisfy the inequality equation.

$$10 – 2x > 18$$

$$-8 > 2x$$

$$-4 > x$$, NOT x > - 4.

I suggest you to read the replies above.
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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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20 Jun 2017, 08:37
Top Contributor
FB2017 wrote:
Since 10 – 2x > 18 is the inequality statement my answer would be (B) x > -4.
Any value greater than -4 will satisfy the inequality equation.

You have fallen into a common trap.

I assume that you first subtracted 10 from each side of the inequality to get: -2x > 8
Then you divided both sides by -2 to get: x > -4
HOWEVER, when you divide both sides on an inequality by a NEGATIVE value, you must REVERSE the direction of the inequality symbol.
So, it should be x < -4

More here:

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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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20 Jun 2017, 08:40
Top Contributor
FB2017 wrote:
Any value greater than -4 will satisfy the inequality equation.

I should also point out that you can always TEST values to confirm (or refute) your conclusion.
You are saying that any value greater than -4 will satisfy the inequality

So, let's see if 0 satisfies the given inequality.
Replace x with 0 to get: 10 – 2(0) > 18
Simplify to get: 10 > 18.
Doesn't work.

Cheers,
Brent
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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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20 Jun 2017, 09:36
Its E.
Fairly a simple question involving flipping of the sign .
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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?  [#permalink]

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20 Jun 2017, 18:16
hirendhanak wrote:
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

We can simplify the given inequality:

10 - 2x > 18

-2x > 8

x < -4

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Re: Which of the following inequalities is equivalent to 10 – 2x > 18?   [#permalink] 20 Jun 2017, 18:16
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