Solve 1/2(90000-7500x)leq8000x

$$\frac{ 1 }{ 2 } (90000-7500x) \leq 8000x$$

Solve for x

$$x\geq \frac{180}{47}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 90000-7500x.

$$\frac{1}{2}\times 90000+\frac{1}{2}\left(-7500\right)x\leq 8000x$$

Multiply \frac{1}{2} and 90000 to get \frac{90000}{2}.

$$\frac{90000}{2}+\frac{1}{2}\left(-7500\right)x\leq 8000x$$

Divide 90000 by 2 to get 45000.

$$45000+\frac{1}{2}\left(-7500\right)x\leq 8000x$$

Multiply \frac{1}{2} and -7500 to get \frac{-7500}{2}.

$$45000+\frac{-7500}{2}x\leq 8000x$$

Divide -7500 by 2 to get -3750.

$$45000-3750x\leq 8000x$$

Subtract 8000x from both sides.

$$45000-3750x-8000x\leq 0$$

Combine -3750x and -8000x to get -11750x.

$$45000-11750x\leq 0$$

Subtract 45000 from both sides. Anything subtracted from zero gives its negation.

$$-11750x\leq -45000$$

Divide both sides by -11750. Since -11750 is negative, the inequality direction is changed.

$$x\geq \frac{-45000}{-11750}$$

Reduce the fraction \frac{-45000}{-11750} to lowest terms by extracting and canceling out -250.

$$x\geq \frac{180}{47}$$