Solve the inequality x-11/3>3x-14/3

x-\frac{1}{3}>3x-\frac{4}{3}

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Answer

$x<\frac{1}{2}$

Step by step solution

Problem

$x-\frac{1}{3}>3x-\frac{4}{3}$
1

Multiply $-1$ times $\frac{1}{3}$

$x-\frac{1}{3}>3x-\frac{4}{3}$
2

Grouping terms

$-3x-\frac{1}{3}+x>-\frac{4}{3}$
3

Adding $-3x$ and $x$

$-2x-\frac{1}{3}>-\frac{4}{3}$
4

Moving the term $-\frac{1}{3}$ to the other side of the inequation with opposite sign

$-2x>\frac{1}{3}-\frac{4}{3}$
5

Subtract the values $\frac{1}{3}$ and $-\frac{4}{3}$

$-2x>-1$
6

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

$2x<1$
7

Divide both sides of the inequation by $2$

$x<\frac{1}{2}$

Answer

$x<\frac{1}{2}$

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Problem Analysis

Main topic:

Inequalities

Time to solve it:

0.27 seconds

Views:

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