Solve 0.1(0.03x+4)geq0.02x+0.434

$$0.1 ( 0.03 x + 4 ) \geq 0.02 x + 0.434$$

Solve for x

$$x\leq -2$$

Solution Steps

Use the distributive property to multiply 0.1 by 0.03x+4.

$$0.003x+0.4\geq 0.02x+0.434$$

Subtract 0.02x from both sides.

$$0.003x+0.4-0.02x\geq 0.434$$

Combine 0.003x and -0.02x to get -0.017x.

$$-0.017x+0.4\geq 0.434$$

Subtract 0.4 from both sides.

$$-0.017x\geq 0.434-0.4$$

Subtract 0.4 from 0.434 to get 0.034.

$$-0.017x\geq 0.034$$

Divide both sides by -0.017. Since -0.017 is negative, the inequality direction is changed.

$$x\leq \frac{0.034}{-0.017}$$

Expand \frac{0.034}{-0.017} by multiplying both numerator and the denominator by 1000.

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

Divide 34 by -17 to get -2.

$$x\leq -2$$