Solve 13-x/7-0.7x-0.2/0.5>1

$$\frac { 13 - x } { 7 } - \frac { 0.7 x - 0.2 } { 0.5 } > 1$$

Solve for x

$$x<\frac{22}{27}$$

Solution Steps

Multiply both sides of the equation by 7. Since 7 is positive, the inequality direction remains the same.

$$13-x-7\times \frac{0.7x-0.2}{0.5}>7$$

Divide each term of 0.7x-0.2 by 0.5 to get \frac{0.7x}{0.5}+\frac{-0.2}{0.5}.

$$13-x-7\left(\frac{0.7x}{0.5}+\frac{-0.2}{0.5}\right)>7$$

Divide 0.7x by 0.5 to get 1.4x.

$$13-x-7\left(1.4x+\frac{-0.2}{0.5}\right)>7$$

Expand \frac{-0.2}{0.5} by multiplying both numerator and the denominator by 10.

$$13-x-7\left(1.4x+\frac{-2}{5}\right)>7$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$13-x-7\left(1.4x-\frac{2}{5}\right)>7$$

Use the distributive property to multiply -7 by 1.4x-\frac{2}{5}.

$$13-x-9.8x-7\left(-\frac{2}{5}\right)>7$$

Express -7\left(-\frac{2}{5}\right) as a single fraction.

$$13-x-9.8x+\frac{-7\left(-2\right)}{5}>7$$

Multiply -7 and -2 to get 14.

$$13-x-9.8x+\frac{14}{5}>7$$

Combine -x and -9.8x to get -10.8x.

$$13-10.8x+\frac{14}{5}>7$$

Convert 13 to fraction \frac{65}{5}.

$$\frac{65}{5}-10.8x+\frac{14}{5}>7$$

Since \frac{65}{5} and \frac{14}{5} have the same denominator, add them by adding their numerators.

$$\frac{65+14}{5}-10.8x>7$$

Add 65 and 14 to get 79.

$$\frac{79}{5}-10.8x>7$$

Subtract \frac{79}{5} from both sides.

$$-10.8x>7-\frac{79}{5}$$

Convert 7 to fraction \frac{35}{5}.

$$-10.8x>\frac{35}{5}-\frac{79}{5}$$

Since \frac{35}{5} and \frac{79}{5} have the same denominator, subtract them by subtracting their numerators.

$$-10.8x>\frac{35-79}{5}$$

Subtract 79 from 35 to get -44.

$$-10.8x>-\frac{44}{5}$$

Divide both sides by -10.8. Since -10.8 is negative, the inequality direction is changed.

$$x<\frac{-\frac{44}{5}}{-10.8}$$

Express \frac{-\frac{44}{5}}{-10.8} as a single fraction.

$$x<\frac{-44}{5\left(-10.8\right)}$$

Multiply 5 and -10.8 to get -54.

$$x<\frac{-44}{-54}$$

Reduce the fraction \frac{-44}{-54} to lowest terms by extracting and canceling out -2.

$$x<\frac{22}{27}$$