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Common monomial factor Calculator

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1

Solved example of common monomial factor

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

Solve the product $-\frac{1}{2}\left(4x-1\right)$

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

Adding $\frac{2}{3}x$ and $-2x$

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

Moving the term $\frac{1}{2}$ to the other side of the inequation with opposite sign

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

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

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

Divide both sides of the inequation by $\frac{4}{3}$

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

Take $\frac{-1}{\frac{4}{3}}$ out of the fraction

$x\leq -\frac{3}{4}\left(x+2\left(x-3\right)-\frac{1}{2}\right)$
8

Solve the product $-\frac{3}{4}\left(x+2\left(x-3\right)-\frac{1}{2}\right)$

$x\leq -\frac{3}{4}x-\frac{3}{4}\left(2\left(x-3\right)-\frac{1}{2}\right)$
9

Solve the product $-\frac{3}{4}\left(2\left(x-3\right)-\frac{1}{2}\right)$

$x\leq -\frac{3}{4}x-\frac{3}{2}\left(x-3\right)+\frac{3}{8}$
10

Grouping terms

$x-\left(-\frac{3}{4}x-\frac{3}{2}\left(x-3\right)\right)\leq \frac{3}{8}$
11

Solve the product $-\left(-\frac{3}{4}x-\frac{3}{2}\left(x-3\right)\right)$

$x+\frac{3}{4}x+\frac{3}{2}\left(x-3\right)\leq \frac{3}{8}$
12

Adding $\frac{3}{4}x$ and $x$

$\frac{7}{4}x+\frac{3}{2}\left(x-3\right)\leq \frac{3}{8}$
13

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

$\frac{7}{4}x+\frac{3}{2}x-\frac{9}{2}\leq \frac{3}{8}$
14

Adding $\frac{7}{4}x$ and $\frac{3}{2}x$

$\frac{13}{4}x-\frac{9}{2}\leq \frac{3}{8}$
15

Moving the term $-\frac{9}{2}$ to the other side of the inequation with opposite sign

$\frac{13}{4}x\leq \frac{39}{8}$
16

Divide both sides of the inequation by $\frac{13}{4}$

$x\leq \frac{3}{2}$

Answer

$x\leq \frac{3}{2}$

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