Question

How do you solve $3x < 5x + 8$?

Answer 1

Hint: The given equation is $3x < 5x + 8$
Add or subtract quantities to obtain the unknown on one side and the numbers on the other.
After that we simplify the equation.
Be careful! Recall that multiplying and dividing an inequality will switch the direction of the inequality sign as well.
Finally we get the $x$ value.

Complete step-by-step solution:
The given equation is $3x < 5x + 8$
We do solve the equation and find the $x$ value.
At first, solve this just like you would an equation.
Let the equation is $3x < 5x + 8$
Subtract by $5x$ on both sides, hence we get
$ \Rightarrow 3x - 5x < 5x + 8 - 5x$
Subtract $3x$ by $5x$ in LHS (Left Hand Side) and subtract $5x$ by $5x$ in RHS (Right Hand Side), hence we get
$ \Rightarrow - 2x < 0 + 8$
The zero terms vanish
$ \Rightarrow - 2x < 8$
Divide by $ - 2$ on both sides, hence we get
$ \Rightarrow \dfrac{{ - \not{2}}}{{ - \not{2}}}x < - \dfrac{8}{2}$
Now, be careful! Recall that multiplying and dividing an inequality will switch the direction of the inequality sign as well.
So, here, the inequality sign will switch from$ < $to$ > $ when we divide by $ - 2$, giving the final inequality:
$ \Rightarrow x > \dfrac{8}{{ - 2}}$
Divide$8$ by $2$, hence we get
$ \Rightarrow x > - 4$

Therefore the simplified form of the inequality is $x > - 4$.

Note: Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol $x = y$, $x$ is equal to $y$.
Where as in inequality, the two expressions are not necessarily equal which is indicated by the symbols:$ > , < , \leqslant $ or $ \geqslant $
$x > y$,$x$ is greater than $y$
$x \geqslant y$,$x$ is greater than or equal to $y$
$x < y$,$x$ is less than $y$
$x \leqslant y$,$x$ is less than or equal to $y$
An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.