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# How do you solve $4x - 2 > 6x + 8$?

Last updated date: 18th Jun 2024
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Hint: In this question, we are given an inequality and we not only have to find the answer, but we also have to write the steps which we will be following to find the answer. Start with shifting the terms on one side such that the terms containing variables are on one side and the constants are on the other side. Then, simplify and find the range of the variable.

Complete step-by-step solution:
We are given an inequality in this question.
$\Rightarrow 4x - 2 > 6x + 8$ …. (Given)
Step 1: Bring the terms containing the variables on one side.
$\Rightarrow - 2 > 6x - 4x + 8$
Step 2: Simplify the equation.
$\Rightarrow - 2 > 2x + 8$
Step 3: Now, shift the constant to the other side, leaving the variable on one side.
$\Rightarrow - 2 - 8 > 2x$
Step 4: Simplify the equation.
$\Rightarrow - 10 > 2x$
$\Rightarrow \dfrac{{ - 10}}{2} > x$
Hence, $x < - 5$.
Therefore, we have the upper limit of the variable x.

Solution for the given inequality is x < -5.

Note: If you find it difficult to shift the terms in an inequality, you can add or subtract the same terms on both the sides. But how will this work? If there is $+ 9$ on one side, and you want to shift it to the other side, simply subtract $9$ on both the sides. This will neutralize the effect and will give you and $0$ on one side, and will give you $- 9$ on the other side. Let us solve this question with this method.
$\Rightarrow 4x - 2 > 6x + 8$
Subtract $8$ on both the sides,
$\Rightarrow 4x - 2 - 8 > 6x + 8 - 8$
On simplifying, we will get,
$\Rightarrow 4x - 10 > 6x$
Now, subtract $4x$ on both the sides,
$\Rightarrow 4x - 4x - 10 > 6x - 4x$
On simplifying, we will get,
$\Rightarrow - 10 > 2x$
Dividing both the sides by $2$,
$\Rightarrow \dfrac{{ - 10}}{2} > \dfrac{{2x}}{2}$
On simplifying, we will get,
$\Rightarrow - 5 > x$
Hence, in this way, we could find the desired value without shifting. But, always remember this that when you change the sign on both the sides, the sign of inequality also changes.