Question

How do you solve the inequality $8-2x<4$ ?

Answer 1

Hint: In this question, we have to find the value of x. It is given that there is an inequation; therefore, we did not get the exact answer of x but will get some range where the values of x lie. Thus, we solve this problem using basic mathematical rules. We will first subtract 8 on both sides of the given inequation. On further calculations, we will multiply (-1) on both sides of the inequation. In the last, we will divide 2 on both sides of the equation and thus get some ranges of x, which is the required result for the problem.

Complete step by step answer:
According to the problem, we have to find the value of x.
So, we will apply the basic mathematical rules to get the solution.
The inequation given to us is $8-2x<4$ ---------- (1)
So, we will first subtract 8 on both sides in the equation (1), we get
$8-2x-8<4-8$
As we know, the same terms with opposite signs cancel out each other, therefore on the left-hand side of the above equation, we get
$-2x<-4$
Now, we will multiply (-1) on both sides in the above equation, we get
$-2x.(-1)>-4.(-1)$
On further simplification, we get
$2x>4$
Now, we will divide 2 on both sides in the above equation, we get
$\dfrac{2x}{2}>\dfrac{4}{2}$
Therefore, we get
$x>2$

Thus, for the inequation $8-2x<4$ , the range for the value of x is $x>2$ . Thus, the range of x in terms of the interval is $(2, \infty)$

Note: While solving this problem, do mention all the formulas you are using to avoid confusion and mathematical errors. Do not forget that it is an inequation, thus we do not get an exact answer instead we will get some range of x.