Question

Solve 2x+8 ≤ 3-3x and show the solution on the number line.​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{2x+8\,\leq\,3-3x}$

$\underline{\textbf{To find:}}$

$\textsf{Solution of}\;\mathsf{2x+8\,\leq\,3-3x}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{2x+8\,\leq\,3-3x}$

$\textsf{This can be written as}$

$\mathsf{2x+3x\,\leq\,3-8}$

$\mathsf{5x\,\leq\,-5}$

$\textsf{Divide throughout by 5}$

$\mathsf{\dfrac{5x}{5}\,\leq\,\dfrac{-5}{5}}$

$\mathsf{x\,\leq\,-1}$

$\therefore\textbf{Solution set is}\;\bf(-\infty,-1]$

Answer 2

Step-by-step explanation:

Let the given equation be number one as it is shown,

$2 x+8 \leq 3-3 x$

Now, subtract 8 on both sides of the equation, as shown below,

$2 x+8-8 \leq 3-3 x-8$

After solving the above equation, we will get, as shown below,

$2 x \leq-3 x-5$

Now, add $3 \mathrm{x}$ on both sides, as shown below,

$2 x+3 x \leq 3 x-3 x-5$

Solving the above equation, we will get, as shown below,

$5 x \leq-5$

Now, divide $5$ into both sides as shown below,

$\frac{5x}{5}\leq \frac{-5}{5}$

Solving the above equation, we will get, as shown below,

$x \leq-1$

Therefore, $x$ should be equal to or smaller than $-1$. Thus, it can be represented on the number line as show below: