# 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:

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

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

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

$8+2x-3x-x\leq 6$
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Adding $2x$ and $-3x$

$-x+8-x\leq 6$
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Adding $-x$ and $-x$

$-2x+8\leq 6$
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Moving the term $8$ to the other side of the inequation with opposite sign

$-2x\leq -2$
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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

~ 0.04 seconds