Solve 10(1000-x)(1+02%x)geq12x

$$10(1000-x)(1+02 \% x) \geq 12x$$

Solve for x

$$x\leq \frac{5000}{11}$$

Solution Steps

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$10\left(1000-x\right)\left(1+0\times \frac{1}{50}x\right)\geq 12x$$

Multiply 0 and \frac{1}{50} to get 0.

$$10\left(1000-x\right)\left(1+0x\right)\geq 12x$$

Anything times zero gives zero.

$$10\left(1000-x\right)\left(1+0\right)\geq 12x$$

Add 1 and 0 to get 1.

$$10\left(1000-x\right)\times 1\geq 12x$$

Multiply 10 and 1 to get 10.

$$10\left(1000-x\right)\geq 12x$$

Use the distributive property to multiply 10 by 1000-x.

$$10000-10x\geq 12x$$

Subtract 12x from both sides.

$$10000-10x-12x\geq 0$$

Combine -10x and -12x to get -22x.

$$10000-22x\geq 0$$

Subtract 10000 from both sides. Anything subtracted from zero gives its negation.

$$-22x\geq -10000$$

Divide both sides by -22. Since -22 is negative, the inequality direction is changed.

$$x\leq \frac{-10000}{-22}$$

Reduce the fraction \frac{-10000}{-22} to lowest terms by extracting and canceling out -2.

$$x\leq \frac{5000}{11}$$