Question

How do you solve $ - 8x > 24 $ ?

Answer 1

Hint: In this question we are asked to solve the inequality, and these type of questions can be solved taking all constant terms to one side and all terms containing \[x\] to the other sides and then simplify the equation till we get the required result.

Complete step by step solution:
Inequalities are mathematical expressions involving the symbols >, <,\[ \geqslant \] ,\[ \leqslant \] To solve an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.
A linear inequality is an inequality in one variable that can be written in one of the following forms where \[a\] and \[b\] are real numbers and \[a \ne 0\] ,
\[ax + b < 0;ax + b > 0;ax + b \geqslant 0;ax + b \leqslant 0\] .
Now the give inequality is $ - 8x > 24 $ ,
Divide both sides with 8, we get,
\[ \Rightarrow \dfrac{{ - 8x}}{8} > \dfrac{{24}}{8}\] ,
Now simplify the equation we get,
\[ \Rightarrow - x > 3\] ,
Now multiply both sides with negative sign we get,
\[ \Rightarrow - \left( { - x} \right) < - 3\] ,
And when we apply negative sign for a greater than sign then it becomes less than and when we apply negative sign for a less than sign then it becomes greater than
Now simplifying we get,
\[ \Rightarrow x < - 3\] ,
This can also be written as \[\left( { - \infty , - 3} \right)\] .

The solution of the given inequality $ - 8x > 24 $ is \[\left( { - \infty , - 3} \right)\]

Note: There are three ways to represent solutions to inequalities: an interval, a graph, and an inequality. Because there is usually more than one solution to an inequality, when you check your answer you should check the end point and one other value to check the direction of the inequality. When we work with inequalities, we can usually treat them similarly to but not exactly as we treat equalities.