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# If $x < 7$, then which option is correctA. $- x < - 7$B. $- x \leqslant - 7$C. $- x > - 7$D. $- x \geqslant - 7$

Last updated date: 22nd Jun 2024
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Hint: In these type of questions the inequalities questions, we have to perform operations like adding, subtracting, multiplying or dividing on both left hand side and right hand side with a variable or number as per the requirement of the question and until we get the required result.

Complete step-by-step solution:
Given expression is $x < 7$,
This is an inequality which can be solved by adding, subtracting, multiplying or dividing both sides till we get the variable that is required.
Now as it is a simple expression, subtract both sides with $x$, we get,
$\Rightarrow x - x < 7 - x$,
Now perform subtracting on both sides we get,
$\Rightarrow 0 < 7 - x$,
Now subtracting both sides with 7, we get,
$\Rightarrow 0 - 7 < 7 - x - 7$,
Now perform subtraction on both sides we get,
$\Rightarrow - 7 < - x$
Now swapping Left hand side with the right side we get,
$\Rightarrow - x > - 7$.
So, the given expression $x < 7$ can be rewritten as $- x > - 7$,

So, option C is correct answer.

Note: We have to solve these types of inequalities by performing addition, subtracting, multiplying or dividing both sides till we get the variable on its own. These operations may change the direction of inequality in two ways, i.e.,
When we perform multiplication or division on both sides by a negative number or putting minus sign on both left hand side and right hand side.
When we do swapping on both the left hand side and right hand side of the given inequality.
And students must be clear that the operations multiplication or division by a variable unless it is clear that it is always positive or always negative.
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