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

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

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Answer

$x\leq \frac{43}{8}$

Step by step solution

Problem

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

Multiply $-1$ times $\frac{4}{5}$

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

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

$-\frac{16}{5}-\frac{4}{5}x+\frac{9}{4}+\frac{3}{2}x\geq \frac{5}{6}x-\frac{5}{3}$
3

Subtract the values $\frac{9}{4}$ and $-\frac{16}{5}$

$-\frac{4}{5}x+\frac{3}{2}x-\frac{19}{20}\geq \frac{5}{6}x-\frac{5}{3}$
4

Adding $\frac{3}{2}x$ and $-\frac{4}{5}x$

$\frac{7}{10}x-\frac{19}{20}\geq \frac{5}{6}x-\frac{5}{3}$
5

Grouping terms

$-\frac{5}{6}x-\frac{19}{20}+\frac{7}{10}x\geq -\frac{5}{3}$
6

Adding $\frac{7}{10}x$ and $-\frac{5}{6}x$

$-\frac{2}{15}x-\frac{19}{20}\geq -\frac{5}{3}$
7

Moving the term $-\frac{19}{20}$ to the other side of the inequation with opposite sign

$-\frac{2}{15}x\geq \frac{19}{20}-\frac{5}{3}$
8

Subtract the values $\frac{19}{20}$ and $-\frac{5}{3}$

$-\frac{2}{15}x\geq -\frac{43}{60}$
9

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

$\frac{2}{15}x\leq \frac{43}{60}$
10

Divide both sides of the inequation by $\frac{2}{15}$

$x\leq \frac{43}{8}$

Answer

$x\leq \frac{43}{8}$

Problem Analysis

Main topic:

Polynomials

Time to solve it:

0.3 seconds

Views:

191