Solve (((6+1.1*6)*1.2*6+x)*1.3*6+x)geq15

$$(((6+1.1 \times 6) \times 1.2 \times 6+x) \times 1.3 \times 6+x) \geq 15$$

Solve for x

$$x\geq -\frac{86577}{1100}$$

Solution Steps

Multiply 1.1 and 6 to get 6.6.

$$\left(\left(6+6.6\right)\times 1.2\times 6+x\right)\times 1.3\times 6+x\geq 15$$

Add 6 and 6.6 to get 12.6.

$$\left(12.6\times 1.2\times 6+x\right)\times 1.3\times 6+x\geq 15$$

Multiply 12.6 and 1.2 to get 15.12.

$$\left(15.12\times 6+x\right)\times 1.3\times 6+x\geq 15$$

Multiply 15.12 and 6 to get 90.72.

$$\left(90.72+x\right)\times 1.3\times 6+x\geq 15$$

Multiply 1.3 and 6 to get 7.8.

$$\left(90.72+x\right)\times 7.8+x\geq 15$$

Use the distributive property to multiply 90.72+x by 7.8.

$$707.616+7.8x+x\geq 15$$

Combine 7.8x and x to get 8.8x.

$$707.616+8.8x\geq 15$$

Subtract 707.616 from both sides.

$$8.8x\geq 15-707.616$$

Subtract 707.616 from 15 to get -692.616.

$$8.8x\geq -692.616$$

Divide both sides by 8.8. Since 8.8 is positive, the inequality direction remains the same.

$$x\geq \frac{-692.616}{8.8}$$

Expand \frac{-692.616}{8.8} by multiplying both numerator and the denominator by 1000.

$$x\geq \frac{-692616}{8800}$$

Reduce the fraction \frac{-692616}{8800} to lowest terms by extracting and canceling out 8.

$$x\geq -\frac{86577}{1100}$$