Solve left(0.8-0.55right)1/2x+left(2-0.7right)x+(x+1/2x)div3*0.15>18

$$\left( 0.8-0.55 \right) \frac{ 1 }{ 2 } x+ \left( 2-0.7 \right) x+(x+ \frac{ 1 }{ 2 } x) \div 3 \times 0.15 > 18$$

Solve for x

$$x>12$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$6\left(0.8-0.55\right)\times \frac{1}{2}x+6\left(2-0.7\right)x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Subtract 0.55 from 0.8 to get 0.25.

$$6\times 0.25\times \frac{1}{2}x+6\left(2-0.7\right)x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Multiply 6 and 0.25 to get 1.5.

$$1.5\times \frac{1}{2}x+6\left(2-0.7\right)x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{2}\times \frac{1}{2}x+6\left(2-0.7\right)x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Multiply \frac{3}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{2\times 2}x+6\left(2-0.7\right)x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Do the multiplications in the fraction \frac{3\times 1}{2\times 2}.

$$\frac{3}{4}x+6\left(2-0.7\right)x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Subtract 0.7 from 2 to get 1.3.

$$\frac{3}{4}x+6\times 1.3x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Multiply 6 and 1.3 to get 7.8.

$$\frac{3}{4}x+7.8x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Combine \frac{3}{4}x and 7.8x to get \frac{171}{20}x.

$$\frac{171}{20}x+2\left(x+\frac{1}{2}x\right)\times 0.15>108$$

Combine x and \frac{1}{2}x to get \frac{3}{2}x.

$$\frac{171}{20}x+2\times \frac{3}{2}x\times 0.15>108$$

Cancel out 2 and 2.

$$\frac{171}{20}x+3x\times 0.15>108$$

Multiply 3 and 0.15 to get 0.45.

$$\frac{171}{20}x+0.45x>108$$

Combine \frac{171}{20}x and 0.45x to get 9x.

$$9x>108$$

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

$$x>\frac{108}{9}$$

Divide 108 by 9 to get 12.

$$x>12$$