Solve the inequality -2x-10(x-3)+3x%6(x-3)+9

{3x-2x-10\left(x-3\right)}\geq {6\left(x-3\right)+9}

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Answer

$x\leq \frac{13}{5}$

Step by step solution

Problem

${3x-2x-10\left(x-3\right)}\geq {6\left(x-3\right)+9}$
1

Multiply $\left(x+-3\right)$ by $-10$

$-2x+3x+30-10x\geq 9-18+6x$
2

Subtract the values $9$ and $-18$

$-2x+3x+30-10x\geq 6x-9$
3

Adding $3x$ and $-2x$

$30-10x+x\geq 6x-9$
4

Adding $-10x$ and $x$

$30-9x\geq 6x-9$
5

Grouping terms

$-6x+30-9x\geq -9$
6

Adding $-9x$ and $-6x$

$30-15x\geq -9$
7

Moving the term $30$ to the other side of the inequation with opposite sign

$-15x\geq -9-30$
8

Subtract the values $-9$ and $-30$

$-15x\geq -39$
9

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

$15x\leq 39$
10

Divide both sides of the inequation by $15$

$x\leq \frac{13}{5}$

Answer

$x\leq \frac{13}{5}$

Problem Analysis

Main topic:

Polynomials

Time to solve it:

0.23 seconds

Views:

194