Solve 70/10012000xleq50/1005+12000(x-5)

$$\frac{ 70 }{ 100 } 12000x \leq \frac{ 50 }{ 100 } 5+12000(x-5)$$

Solve for x

$$x\geq \frac{23999}{1440}$$

Solution Steps

Reduce the fraction \frac{70}{100} to lowest terms by extracting and canceling out 10.

$$\frac{7}{10}\times 12000x\leq \frac{50}{100}\times 5+12000\left(x-5\right)$$

Express \frac{7}{10}\times 12000 as a single fraction.

$$\frac{7\times 12000}{10}x\leq \frac{50}{100}\times 5+12000\left(x-5\right)$$

Multiply 7 and 12000 to get 84000.

$$\frac{84000}{10}x\leq \frac{50}{100}\times 5+12000\left(x-5\right)$$

Divide 84000 by 10 to get 8400.

$$8400x\leq \frac{50}{100}\times 5+12000\left(x-5\right)$$

Reduce the fraction \frac{50}{100} to lowest terms by extracting and canceling out 50.

$$8400x\leq \frac{1}{2}\times 5+12000\left(x-5\right)$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$8400x\leq \frac{5}{2}+12000\left(x-5\right)$$

Use the distributive property to multiply 12000 by x-5.

$$8400x\leq \frac{5}{2}+12000x-60000$$

Convert 60000 to fraction \frac{120000}{2}.

$$8400x\leq \frac{5}{2}+12000x-\frac{120000}{2}$$

Since \frac{5}{2} and \frac{120000}{2} have the same denominator, subtract them by subtracting their numerators.

$$8400x\leq \frac{5-120000}{2}+12000x$$

Subtract 120000 from 5 to get -119995.

$$8400x\leq -\frac{119995}{2}+12000x$$

Subtract 12000x from both sides.

$$8400x-12000x\leq -\frac{119995}{2}$$

Combine 8400x and -12000x to get -3600x.

$$-3600x\leq -\frac{119995}{2}$$

Divide both sides by -3600. Since -3600 is negative, the inequality direction is changed.

$$x\geq \frac{-\frac{119995}{2}}{-3600}$$

Express \frac{-\frac{119995}{2}}{-3600} as a single fraction.

$$x\geq \frac{-119995}{2\left(-3600\right)}$$

Multiply 2 and -3600 to get -7200.

$$x\geq \frac{-119995}{-7200}$$

Reduce the fraction \frac{-119995}{-7200} to lowest terms by extracting and canceling out -5.

$$x\geq \frac{23999}{1440}$$