Solve the inequality (4x-2)/3-1%(5x+4)/6-1(2-7x)/2

{\frac{4x-2}{3}-1}\geq {\frac{5x+4}{6}-\frac{2-7x}{2}}

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Answer

$x\leq -\frac{4}{9}$

Step by step solution

Problem

${\frac{4x-2}{3}-1}\geq {\frac{5x+4}{6}-\frac{2-7x}{2}}$
1

Moving the term $-1$ to the other side of the inequation with opposite sign

$\frac{4x-2}{3}\geq 1-\frac{2-7x}{2}+\frac{4+5x}{6}$
2

Moving the $3$ multiplying to the other side of the inequation

$4x-2\geq 3\left(1-\frac{2-7x}{2}+\frac{4+5x}{6}\right)$
3

Multiply $\left(\frac{4+5x}{6}+-\frac{2-7x}{2}\right)$ by $3$

$4x-2\geq 3-3\frac{2-7x}{2}+3\frac{4+5x}{6}$
4

Simplify the fraction

$4x-2\geq 3-\frac{3}{2}\left(2-7x\right)+\frac{1}{2}\left(4+5x\right)$
5

Multiply $\left(5x+4\right)$ by $\frac{1}{2}$

$4x-2\geq 3+\frac{21}{2}x-3+2+\frac{5}{2}x$
6

Subtract the values $3$ and $-3$

$4x-2\geq \frac{21}{2}x+2+\frac{5}{2}x+0$
7

Add the values $0$ and $2$

$4x-2\geq \frac{21}{2}x+\frac{5}{2}x+2$
8

Adding $\frac{5}{2}x$ and $\frac{21}{2}x$

$4x-2\geq 2+13x$
9

Grouping terms

$-13x-2+4x\geq 2$
10

Adding $4x$ and $-13x$

$-9x-2\geq 2$
11

Moving the term $-2$ to the other side of the inequation with opposite sign

$-9x\geq 2+2$
12

Add the values $2$ and $2$

$-9x\geq 4$
13

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

$9x\leq -4$
14

Divide both sides of the inequation by $9$

$x\leq -\frac{4}{9}$

Answer

$x\leq -\frac{4}{9}$

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Problem Analysis

Main topic:

Polynomials

Time to solve it:

0.3 seconds

Views:

220