Solve 0.2x-0.1/0.3<3x-4/6

$$\frac { 0.2 x - 0.1 } { 0.3 } < \frac { 3 x - 4 } { 6 }$$

Solve for x

$$x<-2$$

Solution Steps

Multiply both sides of the equation by 6. Since 6 is positive, the inequality direction remains the same.

$$6\times \frac{0.2x-0.1}{0.3}<3x-4$$

Divide each term of 0.2x-0.1 by 0.3 to get \frac{0.2x}{0.3}+\frac{-0.1}{0.3}.

$$6\left(\frac{0.2x}{0.3}+\frac{-0.1}{0.3}\right)<3x-4$$

Divide 0.2x by 0.3 to get \frac{2}{3}x.

$$6\left(\frac{2}{3}x+\frac{-0.1}{0.3}\right)<3x-4$$

Expand \frac{-0.1}{0.3} by multiplying both numerator and the denominator by 10.

$$6\left(\frac{2}{3}x+\frac{-1}{3}\right)<3x-4$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$6\left(\frac{2}{3}x-\frac{1}{3}\right)<3x-4$$

Use the distributive property to multiply 6 by \frac{2}{3}x-\frac{1}{3}.

$$4x+6\left(-\frac{1}{3}\right)<3x-4$$

Express 6\left(-\frac{1}{3}\right) as a single fraction.

$$4x+\frac{6\left(-1\right)}{3}<3x-4$$

Multiply 6 and -1 to get -6.

$$4x+\frac{-6}{3}<3x-4$$

Divide -6 by 3 to get -2.

$$4x-2<3x-4$$

Subtract 3x from both sides.

$$4x-2-3x<-4$$

Combine 4x and -3x to get x.

$$x-2<-4$$

Add 2 to both sides.

$$x<-4+2$$

Add -4 and 2 to get -2.

$$x<-2$$