Question

Solve:$1 < 3x + 4 < 10$?

Answer 1

Hint: The range for values of x in $1 < 3x + 4 < 10$ can be found by using the method of transposition. Method of transposition involves doing the exact same mathematical thing on all sides of an equation or inequality with the aim of simplification in mind. This method can be used to solve various algebraic inequalities like the one given in question with ease.

Complete step-by-step solution:
In the given question, we are required to solve an inequality. Such inequalities can be solved using the algebraic rules such as transposition which involves doing the exact same mathematical thing on all sides of an equation or inequality with the aim of simplification in mind.
Now, we need to remove 4 from the middle entry by subtracting $4$. Thus, subtracting 4 from each side of inequality, we get,
$\Rightarrow 1 - 4 < 3x + 4 - 4 < 10 - 4$
$ \Rightarrow - 3 < 3x < 6$
Now, to find the value of x, we need to isolate the variable. We do so by dividing all the sides of the inequality by $3$.
Thus dividing each entry by $3$, we get,
$ \Rightarrow \dfrac{{ - 3}}{3} < \dfrac{{3x}}{3} < \dfrac{6}{3}$
$ \Rightarrow - 1 < x < 2$
Therefore the value of x is more than $ - 1$ and less than $2$.
Hence, the range of values of x is $\left( { - 1,2} \right)$

Note: There is no fixed way of solving a given algebraic inequality. Algebraic inequality can be solved in various ways. Linear equations in one variable can be solved by the transposition method with ease. If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal.