Question

Solve $\dfrac{w}{6} > - 3$?

Answer 1

Hint: We will have to solve for $w$ simply by solving the above equation, not just as an equation but with keeping inequality in mind, i.e., the addition or subtraction of variables and constants on both sides rather than simply transposing them. Multiply both sides by the coefficient of the denominator to solve for $w$.

Complete step by step answer:
A linear inequality is a mathematical statement that relates a linear expression as either less than or greater than another.
A solution to a linear inequality is a real number that will produce a true statement when substituted for the variable. Linear inequalities have either infinitely many solutions or no solution. If there are infinitely many solutions, graph the solution set on a number line and/or express the solution using interval notation.
Here, we have the given inequality of the form
$ \Rightarrow \dfrac{w}{6} > - 3$
In the above equation, we could have simply transposed the RHS variables to LHS but that is inappropriate for an inequality-based equation.
Multiplying both sides by 6, we get
$ \Rightarrow \dfrac{w}{6} \times 6 > - 3 \times 6$
Simplify the terms,
$ \Rightarrow w > - 18$
Hence, we can say that the value of real $w$ with given inequality is $w \in \left[ { - 18,\infty } \right)$.

Note: A simple mistake that is very common in this kind of problem is, students generally transpose the variables across the inequality like a normal equation which is not preferred, especially in the case of multiplications and divisions.
The arithmetic symbols, < is less than symbol, > is the greater than symbol and = is the equal to symbol. Suppose if the inequality involves $x < a$, this tells that the value of x should not exceed than the number a. if the inequality involves $x > a$, this tells that the value of x should take the number greater than the number a. if the inequality involves $x = a$, this tells that the value of x should be equal to the number a.