# Step-by-step Solution

## Solve the inequality $2\left(x+1\right)-3\left(x-2\right)\leq x+6$

Go!
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### Videos

$x\geq 1$

## Step-by-step explanation

Problem to solve:

$2\left(x+1\right)-3\left(x-2\right)\leq x+6$
1

Grouping terms

$2\left(x+1\right)-3\left(x-2\right)-x\leq 6$
2

Solve the product $2\left(x+1\right)$

$2x+2-3\left(x-2\right)-x\leq 6$
3

Adding $2x$ and $-1x$

$x+2-3\left(x-2\right)\leq 6$
4

Solve the product $-3\left(x-2\right)$

$8+x-3x\leq 6$
5

Adding $-3x$ and $x$

$-2x+8\leq 6$
6

Moving the term $8$ to the other side of the inequation with opposite sign

$-2x\leq -2$
7

Multiply both sides of the inequality by $-1$, reversing the sign

$2x\geq 2$
8

Divide both sides of the inequation by $2$

$x\geq 1$

$x\geq 1$

### Problem Analysis

$2\left(x+1\right)-3\left(x-2\right)\leq x+6$

Inequalities

~ 1.59 seconds