Solve 1/5*2+5x-6=2/3-5+10x-15

$$\frac{ 1 }{ 5 } \times 2+5x-6= \frac{ 2 }{ 3 } -5+10x-15$$

Solve for x

$$x = \frac{206}{75} = 2\frac{56}{75} \approx 2.746666667$$

Steps for Solving Linear Equation

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

$$\frac{2}{5}+5x-6=\frac{2}{3}-5+10x-15$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{2}{5}+5x-\frac{30}{5}=\frac{2}{3}-5+10x-15$$

Since \frac{2}{5} and \frac{30}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-30}{5}+5x=\frac{2}{3}-5+10x-15$$

Subtract 30 from 2 to get -28.

$$-\frac{28}{5}+5x=\frac{2}{3}-5+10x-15$$

Convert 5 to fraction \frac{15}{3}.

$$-\frac{28}{5}+5x=\frac{2}{3}-\frac{15}{3}+10x-15$$

Since \frac{2}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{28}{5}+5x=\frac{2-15}{3}+10x-15$$

Subtract 15 from 2 to get -13.

$$-\frac{28}{5}+5x=-\frac{13}{3}+10x-15$$

Convert 15 to fraction \frac{45}{3}.

$$-\frac{28}{5}+5x=-\frac{13}{3}+10x-\frac{45}{3}$$

Since -\frac{13}{3} and \frac{45}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{28}{5}+5x=\frac{-13-45}{3}+10x$$

Subtract 45 from -13 to get -58.

$$-\frac{28}{5}+5x=-\frac{58}{3}+10x$$

Subtract 10x from both sides.

$$-\frac{28}{5}+5x-10x=-\frac{58}{3}$$

Combine 5x and -10x to get -5x.

$$-\frac{28}{5}-5x=-\frac{58}{3}$$

Add \frac{28}{5} to both sides.

$$-5x=-\frac{58}{3}+\frac{28}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{58}{3} and \frac{28}{5} to fractions with denominator 15.

$$-5x=-\frac{290}{15}+\frac{84}{15}$$

Since -\frac{290}{15} and \frac{84}{15} have the same denominator, add them by adding their numerators.

$$-5x=\frac{-290+84}{15}$$

Add -290 and 84 to get -206.

$$-5x=-\frac{206}{15}$$

Divide both sides by -5.

$$x=\frac{-\frac{206}{15}}{-5}$$

Express \frac{-\frac{206}{15}}{-5} as a single fraction.

$$x=\frac{-206}{15\left(-5\right)}$$

Multiply 15 and -5 to get -75.

$$x=\frac{-206}{-75}$$

Fraction \frac{-206}{-75} can be simplified to \frac{206}{75} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{206}{75}$$