Solve 1.5x-1/0.3-9x+2/6leq1

$$\frac { 1.5 x - 1 } { 0.3 } - \frac { 9 x + 2 } { 6 } \leq 1$$

Solve for x

$$x\leq \frac{4}{3}$$

Solution Steps

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

$$6\times \frac{1.5x-1}{0.3}-\left(9x+2\right)\leq 6$$

To find the opposite of 9x+2, find the opposite of each term.

$$6\times \frac{1.5x-1}{0.3}-9x-2\leq 6$$

Divide each term of 1.5x-1 by 0.3 to get \frac{1.5x}{0.3}+\frac{-1}{0.3}.

$$6\left(\frac{1.5x}{0.3}+\frac{-1}{0.3}\right)-9x-2\leq 6$$

Divide 1.5x by 0.3 to get 5x.

$$6\left(5x+\frac{-1}{0.3}\right)-9x-2\leq 6$$

Expand \frac{-1}{0.3} by multiplying both numerator and the denominator by 10.

$$6\left(5x+\frac{-10}{3}\right)-9x-2\leq 6$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$6\left(5x-\frac{10}{3}\right)-9x-2\leq 6$$

Use the distributive property to multiply 6 by 5x-\frac{10}{3}.

$$30x+6\left(-\frac{10}{3}\right)-9x-2\leq 6$$

Express 6\left(-\frac{10}{3}\right) as a single fraction.

$$30x+\frac{6\left(-10\right)}{3}-9x-2\leq 6$$

Multiply 6 and -10 to get -60.

$$30x+\frac{-60}{3}-9x-2\leq 6$$

Divide -60 by 3 to get -20.

$$30x-20-9x-2\leq 6$$

Combine 30x and -9x to get 21x.

$$21x-20-2\leq 6$$

Subtract 2 from -20 to get -22.

$$21x-22\leq 6$$

Add 22 to both sides.

$$21x\leq 6+22$$

Add 6 and 22 to get 28.

$$21x\leq 28$$

Divide both sides by 21. Since 21 is positive, the inequality direction remains the same.

$$x\leq \frac{28}{21}$$

Reduce the fraction \frac{28}{21} to lowest terms by extracting and canceling out 7.

$$x\leq \frac{4}{3}$$