Answer

Verified

428.1k+ views

**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.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a labelled sketch of the human eye class 12 physics CBSE