Question

Solve the following question in detail:
How do you solve \[3x + 2 < - 11\]?

Answer 1

Hint: Take the given statement and identify if it is an equation or an inequality. We have to solve for the variable in either case. Then bring the constants of the inequality or the equation to one side of the statement and the variables to the other side of the inequality. We then simplify it until we get the value of the variable either in inequality or the equation.

Complete step-by-step solution:
Given equation;
\[3x + 2 < - 11\]
Now, we have to find the inequality for \[x\]
For that, we have to bring the \[x\] which is the variable to the left-hand side and all the constants to the right-hand side.
For the starters, subtracting \[2\] on both the sides of the inequality, we get;
$\Rightarrow$\[3x + 2 - 2 < - 11 - 2\]
Now, simplifying the equation, we get;
$\Rightarrow$\[3x < - 13\]
To eliminate the coefficient of the variable, we divide the both sides of the inequality with the co-efficient. Then, we get;
$\Rightarrow$\[\dfrac{{3x}}{3} < \dfrac{{ - 13}}{3}\]
Now, cancelling the common terms in the numerator and the denominator, we get;
$\Rightarrow$\[x < \dfrac{{ - 13}}{3}\]

Therefore, we have the inequality for the variable, i.e.,
\[x < \dfrac{{ - 13}}{3}\]

Note: The question asked above is a simple inequality. In a simple inequality with only one variable, we have to solve for it by adding, subtracting. Multiplying or dividing the both sides of the inequality until the variable on the either side is left on its own with no further simplification. It tells us about the size or the value if it is greater than, less than or equal to a certain constant or a set of constants.