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One-variable linear inequalities Calculator

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1

Here, we show you a step-by-step solved example of one-variable linear inequalities. This solution was automatically generated by our smart calculator:

$\frac{1}{2}x+3\le\frac{3}{4}x-2$

Multiplying the fraction by $x$

$\frac{1x}{2}+3\leq \frac{3}{4}x-2$

Any expression multiplied by $1$ is equal to itself

$\frac{x}{2}+3\leq \frac{3}{4}x-2$
2

Multiplying the fraction by $x$

$\frac{x}{2}+3\leq \frac{3}{4}x-2$
3

Moving the term $3$ to the other side of the inequation with opposite sign

$\frac{x}{2}\leq \frac{3}{4}x-2-3$
4

Subtract the values $-2$ and $-3$

$\frac{x}{2}\leq \frac{3}{4}x-5$

Multiplying the fraction by $x$

$\frac{x}{2}\leq \frac{3x}{4}-5$

Multiplying the fraction by $x$

$\frac{1x}{2}+3\leq \frac{3}{4}x-2$

Any expression multiplied by $1$ is equal to itself

$\frac{x}{2}+3\leq \frac{3}{4}x-2$
5

Multiplying the fraction by $x$

$\frac{x}{2}\leq \frac{3x}{4}-5$
6

Grouping terms

$\frac{x}{2}-\frac{3x}{4}\leq -5$
7

Multiplying the fraction by $-1$

$\frac{x}{2}+\frac{-3x}{4}\leq -5$
8

The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

$L.C.M.=4$
9

Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete

$\frac{2x}{4}+\frac{-3x}{4}$

Rewrite the sum of fractions as a single fraction with the same denominator

$\frac{2x-3x}{4}\leq -5$

Combining like terms $2x$ and $-3x$

$\frac{-x}{4}\leq -5$
10

Combine and simplify all terms in the same fraction with common denominator $4$

$\frac{-x}{4}\leq -5$
11

Moving the $4$ multiplying to the other side of the inequation

$-x\leq -5\cdot 4$
12

Multiply $-5$ times $4$

$-x\leq -20$
13

Divide both sides of the inequation by $-1$

$x\leq \frac{-20}{-1}$
14

Divide $-20$ by $-1$

$x\leq 20$

Final answer to the problem

$x\leq 20$

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