Solve the inequality 2(x+1)-3(x-2)#x+6

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

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Answer

$x\geq 1$

Step by step solution

Problem

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

Multiply $\left(x+1\right)$ by $2$

$6-3x+2+2x\leq 6+x$
2

Add the values $2$ and $6$

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

Adding $2x$ and $-3x$

$8-x\leq 6+x$
4

Grouping terms

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

Adding $-x$ and $-x$

$8-2x\leq 6$
6

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

$-2x\leq 6-8$
7

Subtract the values $6$ and $-8$

$-2x\leq -2$
8

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

$2x\geq 2$
9

Divide both sides of the inequation by $2$

$x\geq 1$

Answer

$x\geq 1$

Problem Analysis

Main topic:

Polynomials

Time to solve it:

0.22 seconds

Views:

96