Solve 0.2x-1/7-0.3x/2leq0.1

$$\frac{ 0.2x-1 }{ 7 } - \frac{ 0.3x }{ 2 } \leq 0.1$$

Solve for x

$$x\geq -2$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 7,2. Since 14 is positive, the inequality direction remains the same.

$$2\left(0.2x-1\right)-7\times 0.3x\leq 1.4$$

Use the distributive property to multiply 2 by 0.2x-1.

$$0.4x-2-7\times 0.3x\leq 1.4$$

Multiply -7 and 0.3 to get -2.1.

$$0.4x-2-2.1x\leq 1.4$$

Combine 0.4x and -2.1x to get -1.7x.

$$-1.7x-2\leq 1.4$$

Add 2 to both sides.

$$-1.7x\leq 1.4+2$$

Add 1.4 and 2 to get 3.4.

$$-1.7x\leq 3.4$$

Divide both sides by -1.7. Since -1.7 is negative, the inequality direction is changed.

$$x\geq \frac{3.4}{-1.7}$$

Expand \frac{3.4}{-1.7} by multiplying both numerator and the denominator by 10.

$$x\geq \frac{34}{-17}$$

Divide 34 by -17 to get -2.

$$x\geq -2$$