Question

How do you solve $x - 8 > 10$ ?

Answer 1

Hint: In this question we will isolate the term $x$ , on one side of the inequation to get the final solution. We take the variable value on one side and the constant value on the other side. After separating the variable and constant, we will perform arithmetic operations if required to get the final solution.

Complete step-by-step solution:
We have the given inequation as:
$x - 8 > 10$
Now, since this is a linear inequation we can perform operations on it similar to how we do on an equation.
Now, to isolate the term $x$ , we will transfer the term $8$ from the left-hand side to the right-hand side, we get:
$x > 10 + 8$
On adding the terms in the right-hand side, we get:
Hence, $x > 18$ , is the required solution.

$x > 18$ is the solution for the given problem.

Note: In the above question, we have an inequation, which is different from the general what we call an equation.
An equation equates both the terms on the left-hand side and the right-hand side equally, whereas in inequalities, the left-hand side and right-hand side are not the same to each other.
Inequations can have the greater than sign which is $ > $ and the lesser than sign which is $ < $ .
There can also be the greater than or equal to sign, which is $ \geqslant $ and the lesser than or equal to sign which is $ \leqslant $ .
The solution $x > 18$ implies that the value of should be greater than $18$ , it implies that the value of $x$ can be any other number which is more than $18$ is an incorrect solution to the statement.
Now since the value of $x$ has to be greater than $18$ , $18$ itself does not satisfy this condition,
Because in the expression we have a strictly greater than sign, and not greater than or equal to sign.
If the equation was $x \geqslant 18$ then $18$ would have been the part of the solution.