Solve 2x-0.5/0.5-2x-1.4/0.2>0.5+0.5-x/0.28

$$\frac { 2 x - 0.5 } { 0.5 } - \frac { 2 x - 1.4 } { 0.2 } > 0.5 + \frac { 0.5 - x } { 0.28 }$$

Solve for x

$$x<\frac{26}{17}$$

Solution Steps

Divide each term of 2x-0.5 by 0.5 to get \frac{2x}{0.5}+\frac{-0.5}{0.5}.

$$\frac{2x}{0.5}+\frac{-0.5}{0.5}-\frac{2x-1.4}{0.2}>0.5+\frac{0.5-x}{0.28}$$

Divide 2x by 0.5 to get 4x.

$$4x+\frac{-0.5}{0.5}-\frac{2x-1.4}{0.2}>0.5+\frac{0.5-x}{0.28}$$

Divide -0.5 by 0.5 to get -1.

$$4x-1-\frac{2x-1.4}{0.2}>0.5+\frac{0.5-x}{0.28}$$

Divide each term of 2x-1.4 by 0.2 to get \frac{2x}{0.2}+\frac{-1.4}{0.2}.

$$4x-1-\left(\frac{2x}{0.2}+\frac{-1.4}{0.2}\right)>0.5+\frac{0.5-x}{0.28}$$

Divide 2x by 0.2 to get 10x.

$$4x-1-\left(10x+\frac{-1.4}{0.2}\right)>0.5+\frac{0.5-x}{0.28}$$

Expand \frac{-1.4}{0.2} by multiplying both numerator and the denominator by 10.

$$4x-1-\left(10x+\frac{-14}{2}\right)>0.5+\frac{0.5-x}{0.28}$$

Divide -14 by 2 to get -7.

$$4x-1-\left(10x-7\right)>0.5+\frac{0.5-x}{0.28}$$

To find the opposite of 10x-7, find the opposite of each term.

$$4x-1-10x-\left(-7\right)>0.5+\frac{0.5-x}{0.28}$$

The opposite of -7 is 7.

$$4x-1-10x+7>0.5+\frac{0.5-x}{0.28}$$

Combine 4x and -10x to get -6x.

$$-6x-1+7>0.5+\frac{0.5-x}{0.28}$$

Add -1 and 7 to get 6.

$$-6x+6>0.5+\frac{0.5-x}{0.28}$$

Divide each term of 0.5-x by 0.28 to get \frac{0.5}{0.28}+\frac{-x}{0.28}.

$$-6x+6>0.5+\frac{0.5}{0.28}+\frac{-x}{0.28}$$

Expand \frac{0.5}{0.28} by multiplying both numerator and the denominator by 100.

$$-6x+6>0.5+\frac{50}{28}+\frac{-x}{0.28}$$

Reduce the fraction \frac{50}{28} to lowest terms by extracting and canceling out 2.

$$-6x+6>0.5+\frac{25}{14}+\frac{-x}{0.28}$$

Divide -x by 0.28 to get -\frac{25}{7}x.

$$-6x+6>0.5+\frac{25}{14}-\frac{25}{7}x$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$-6x+6>\frac{1}{2}+\frac{25}{14}-\frac{25}{7}x$$

Least common multiple of 2 and 14 is 14. Convert \frac{1}{2} and \frac{25}{14} to fractions with denominator 14.

$$-6x+6>\frac{7}{14}+\frac{25}{14}-\frac{25}{7}x$$

Since \frac{7}{14} and \frac{25}{14} have the same denominator, add them by adding their numerators.

$$-6x+6>\frac{7+25}{14}-\frac{25}{7}x$$

Add 7 and 25 to get 32.

$$-6x+6>\frac{32}{14}-\frac{25}{7}x$$

Reduce the fraction \frac{32}{14} to lowest terms by extracting and canceling out 2.

$$-6x+6>\frac{16}{7}-\frac{25}{7}x$$

Add \frac{25}{7}x to both sides.

$$-6x+6+\frac{25}{7}x>\frac{16}{7}$$

Combine -6x and \frac{25}{7}x to get -\frac{17}{7}x.

$$-\frac{17}{7}x+6>\frac{16}{7}$$

Subtract 6 from both sides.

$$-\frac{17}{7}x>\frac{16}{7}-6$$

Convert 6 to fraction \frac{42}{7}.

$$-\frac{17}{7}x>\frac{16}{7}-\frac{42}{7}$$

Since \frac{16}{7} and \frac{42}{7} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{17}{7}x>\frac{16-42}{7}$$

Subtract 42 from 16 to get -26.

$$-\frac{17}{7}x>-\frac{26}{7}$$

Divide both sides by -\frac{17}{7}. Since -\frac{17}{7} is negative, the inequality direction is changed.

$$x<\frac{-\frac{26}{7}}{-\frac{17}{7}}$$

Express \frac{-\frac{26}{7}}{-\frac{17}{7}} as a single fraction.

$$x<\frac{-26}{7\left(-\frac{17}{7}\right)}$$

Multiply 7 and -\frac{17}{7} to get -17.

$$x<\frac{-26}{-17}$$

Fraction \frac{-26}{-17} can be simplified to \frac{26}{17} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{26}{17}$$