Question

How do you solve $3x-3\le 6$ ?

Answer 1

In the equation we have an inequality i.e., less than or equal to. In the given expression we can observe the two arithmetic operations first one is multiplication and the second one is subtractions. According to the BODMAS rule we will first apply subtraction and second multiplication. To solve the inequality, we need to apply the reverse operations for the given operations. The first operation is subtraction, so we will perform the addition operation on both sides of the expression similarly we will apply the division operation for multiplication operation. Now we will get our required result.

Complete step-by-step solution:
Given that, $3x-3\le 6$.
In the above expression we have subtracting $3$ on the left side. To solve the above expression, we need to add the same $3$ on both sides. Then we will get
$\Rightarrow 3x-3+3\le 6+3$
We know that $+x-x=0$, then we will have
$\Rightarrow 3x\le 9$
In the above simplified expression, we can observe that $3$ is multiplying $x$ on LHS. To solve the above expression, we will divide the same $3$ on both sides. Then we will have
$\Rightarrow \dfrac{3x}{3}\le \dfrac{9}{3}$
We know that $\dfrac{a}{a}=1$, then we will get
$\therefore x\le 3$.
Hence, we can write the solution of the given equation $3x-3\le 6$ as $x=3$, $x <3$.

Note: We can check whether the obtained result is right or wrong by plugging in any value in the given expression and checking the condition. Let us take the value $2$ as $j$. Then the value of $3x$ will be $\begin{aligned} & 3x=3\times 2 \\\ & \Rightarrow 3x=6 \\\ \end{aligned}$
And the value of $3x-3$ is given by
$\begin{aligned} & 3x-3=6-3 \\\ & \Rightarrow 3x-3=3<6 \\\ \end{aligned}$
Hence the obtained result is correct.