Question

How do you solve the Inequality $5q+7\le 3\left( q+1 \right)$?

Answer 1

Hint: In this question we have been given with an expression which represents an inequation. An inequation is an equation which does not have a $=$ sign. We will solve the expression by multiplying the terms in the right-hand side and simplifying them, we will then take the terms together and simplify their values to get the required solution.

Complete step by step answer:
We have the given inequation as:
$\Rightarrow 5q+7\le 3\left( q+1 \right)$
On simplifying the terms in the right-hand side of the expression, we get:
$\Rightarrow 5q+7\le 3\times q+3\times 1$
On simplifying the terms, we get:
$\Rightarrow 5q+7\le 3q+3$
On transferring the term $3q$ from the right-hand side to the left-hand side, we get:
$\Rightarrow 5q-3q+7\le 3$
On transferring the term $7$ from the left-hand side to the right-hand side, we get:
$\Rightarrow 5q-3q\le 3-7$
On simplifying the terms on the right-hand side and the left-hand side, we get:
$\Rightarrow 2q\le -4$
On transferring the term $2$ from the left-hand side to the right-hand side, we get:
$\Rightarrow q\le \dfrac{-4}{2}$
On simplifying, we get:
$\Rightarrow q\le -2$, which is the required solution.

Note: In the above question we have an inequation, which is different from the general what we call an equation.
An equation equates both the terms on the left-hand side and the right-hand side equally, whereas in inequalities, the left-hand side and right-hand side are not the same to each other.
Inequations can have the greater than sign which is $>$ and the lesser than sign which is $<$.
There can also be the greater than or equal to sign, which is $\ge $ and the lesser than or equal to sign which is $\le $.
The solution $q\le -2$ implies that the value of $q$ should be less than $-2$, it implies that as soon as the value of $q$ is written as more than $-2$, the inequality would differ.