Final Answer
$x\geq 1$
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Step-by-step Solution
Specify the solving method
1
Multiply the single term $2$ by each term of the polynomial $\left(x+1\right)$
$2x+2-3\left(x-2\right)\leq x+6$
2
Multiply the single term $-3$ by each term of the polynomial $\left(x-2\right)$
$2x+2-3x+6\leq x+6$
3
Add the values $2$ and $6$
$8+2x-3x\leq x+6$
4
Combining like terms $2x$ and $-3x$
$8-x\leq x+6$
5
Grouping terms
$8-x-x\leq 6$
6
Combining like terms $-x$ and $-x$
$8-2x\leq 6$
7
Moving the term $8$ to the other side of the inequation with opposite sign
$-2x\leq 6-8$
8
Subtract the values $6$ and $-8$
$-2x\leq -2$
9
Multiply both sides of the inequality by $-1$, reversing the sign
$2x\geq 2$
10
Divide both sides of the inequation by $2$
$x\geq \frac{2}{2}$
11
Divide $2$ by $2$
$x\geq 1$
Final Answer
$x\geq 1$