Solve 0.3y-0.1/0.4-1=5y-7/6

$$\frac { 0.3 y - 0.1 } { 0.4 } - 1 = \frac { 5 y - 7 } { 6 }$$

Solve for y

$$y=-1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$6\times \frac{0.3y-0.1}{0.4}-6=5y-7$$

Divide each term of 0.3y-0.1 by 0.4 to get \frac{0.3y}{0.4}+\frac{-0.1}{0.4}.

$$6\left(\frac{0.3y}{0.4}+\frac{-0.1}{0.4}\right)-6=5y-7$$

Divide 0.3y by 0.4 to get 0.75y.

$$6\left(0.75y+\frac{-0.1}{0.4}\right)-6=5y-7$$

Expand \frac{-0.1}{0.4} by multiplying both numerator and the denominator by 10.

$$6\left(0.75y+\frac{-1}{4}\right)-6=5y-7$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$6\left(0.75y-\frac{1}{4}\right)-6=5y-7$$

Use the distributive property to multiply 6 by 0.75y-\frac{1}{4}.

$$4.5y+6\left(-\frac{1}{4}\right)-6=5y-7$$

Express 6\left(-\frac{1}{4}\right) as a single fraction.

$$4.5y+\frac{6\left(-1\right)}{4}-6=5y-7$$

Multiply 6 and -1 to get -6.

$$4.5y+\frac{-6}{4}-6=5y-7$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$4.5y-\frac{3}{2}-6=5y-7$$

Convert 6 to fraction \frac{12}{2}.

$$4.5y-\frac{3}{2}-\frac{12}{2}=5y-7$$

Since -\frac{3}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$4.5y+\frac{-3-12}{2}=5y-7$$

Subtract 12 from -3 to get -15.

$$4.5y-\frac{15}{2}=5y-7$$

Subtract 5y from both sides.

$$4.5y-\frac{15}{2}-5y=-7$$

Combine 4.5y and -5y to get -0.5y.

$$-0.5y-\frac{15}{2}=-7$$

Add \frac{15}{2} to both sides.

$$-0.5y=-7+\frac{15}{2}$$

Convert -7 to fraction -\frac{14}{2}.

$$-0.5y=-\frac{14}{2}+\frac{15}{2}$$

Since -\frac{14}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$-0.5y=\frac{-14+15}{2}$$

Add -14 and 15 to get 1.

$$-0.5y=\frac{1}{2}$$

Divide both sides by -0.5.

$$y=\frac{\frac{1}{2}}{-0.5}$$

Divide \frac{1}{2} by -0.5 to get -1.

$$y=-1$$