# To find: The solution of the inequality and interval notation. The given inequality equation is: displaystyle{2}{left({x}-{3}right)}-{5}le{3}{left({x}+{2}right)}-{18}

To find: The solution of the inequality and interval notation.
The given inequality equation is:
$2\left(x-3\right)-5\le 3\left(x+2\right)-18$
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Consider the following steps to solve linear inequality in one variable:
If an inequality contains fractions or decimals, multiply both sides by the LCD to clear the equation of fractions or decimals.
Use the distributive property to remove parentheses if they are present.
Simplify each side of the inequality by comining like terms.
Get all variable terms on one side and all numbers on the other side by using the addition property of inequality.
Get the variable alone by using the multiplication property of inequality.
The given inequality equation is,
$2\left(x-3\right)-5\le 3\left(x+2\right)-18$
$2\cdot x-2\cdot 3-5\le 3\cdot x+3\cdot 2-18$
$2x-6-5\le 3x+6-18$
$2x-11-3x\le 3x-12-3x$
Simplify further,
$-x-11\le -12$
$-x-11+11\le -12+11$
$\frac{-x}{-1}\ge \frac{-1}{-1}$
$x\ge 1$
The interval notation of the inequality is written as $\left[1,\mathrm{\infty }\right).$
Therefore, the solution of the inequality is