Question

How do you solve $12x<22+x$ ?

Answer 1

Hint: Here, both of the sides of the inequality contain $x$ terms. So, at first, we bring the $x$ term to the right hand side of the inequality by subtracting it from both sides of the inequality. The, we divide both sides of the inequality by $11$ and get the final solution in terms of another inequality.

Complete step by step solution:
The given inequality that we have at our disposal is
$12x<22+x$
Now, we know that solving an inequality is quite similar to solving an equation. All the operations remain the same except that in inequality, if we multiply or divide both sides by a negative number, or take reciprocals, we need to reverse the inequality sign. So, keeping these in mind, we start off with the solution.
At first, we subtract $x$ from both sides of the inequality. The inequality thus after rewriting becomes,
$\Rightarrow 12x-x < 22+x-x$
The above inequality upon simplification gives,
$\Rightarrow 11x < 22$
Now, we divide both sides of the inequality by $11$ and the inequality thus after rewriting becomes,
$\Rightarrow \dfrac{11x}{11} < \dfrac{22}{11}$
The above inequality simplification gives,
$\Rightarrow x < 2$
This means all values of $x$ less than $3$ , satisfy the given inequality.
Therefore, we can conclude that the solution of the given inequality is $x < 2$ .

Note:
Its better if we cross check our solution by putting a random value of the solution in the given inequality and see if it really satisfies the inequality or not. Also, this problem can be solved by taking the two sides as two equations and then solving them graphically.