Question

Solve for $x$ : $-2x>6$

• A. $x<-3$
• B. $x>-3$
• C. $x<3$

Answer 1

The correct option is A $x<-3$

Method 1:

$-2x>6$

In an inequality, by multiplying both side by $-1$ the sign of inequality gets reversed.

$(-1)\times (-2x)<(-1)\times 6$
$\Rightarrow 2x<-6$

Dividing both side by 2 we get,

$\frac{2x}{2}<\frac{-6}{2}$
$\Rightarrow x<-3$

Method 2:

Similarly when both side of an inequality is divided by a negative number, the sign of inequality changes.

$-2x>6$
$\Rightarrow \frac{-2x}{-2}<\frac{6}{-2}$
$\Rightarrow x<-3$

Method 3:

Step 1: Adding or subtracting same thing to both side of the inequality does not change the sign.

$-2x>6+2x=+2x0\ge 6+2x$

Step 2: Now, adding $-6$ to both the side,

$0>6+2x-6=-6-6>+2x$

Step 3: Divide the both side of the inequality by 2.

$-6>2x$
$\Rightarrow \frac{-6}{2}>\frac{2x}{2}$
$\Rightarrow -3>x$
$\Rightarrow x<-3$