Solve 1.8(1100-x)geq1.2(1+25%)x

$$1.8(1100-x) \geq 1.2(1+25 \% )x$$

Solve for x

$$x\leq 600$$

Solution Steps

Use the distributive property to multiply 1.8 by 1100-x.

$$1980-1.8x\geq 1.2\left(1+\frac{25}{100}\right)x$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$1980-1.8x\geq 1.2\left(1+\frac{1}{4}\right)x$$

Convert 1 to fraction \frac{4}{4}.

$$1980-1.8x\geq 1.2\left(\frac{4}{4}+\frac{1}{4}\right)x$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$1980-1.8x\geq 1.2\times \frac{4+1}{4}x$$

Add 4 and 1 to get 5.

$$1980-1.8x\geq 1.2\times \frac{5}{4}x$$

Convert decimal number 1.2 to fraction \frac{12}{10}. Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$1980-1.8x\geq \frac{6}{5}\times \frac{5}{4}x$$

Multiply \frac{6}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$1980-1.8x\geq \frac{6\times 5}{5\times 4}x$$

Cancel out 5 in both numerator and denominator.

$$1980-1.8x\geq \frac{6}{4}x$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$1980-1.8x\geq \frac{3}{2}x$$

Subtract \frac{3}{2}x from both sides.

$$1980-1.8x-\frac{3}{2}x\geq 0$$

Combine -1.8x and -\frac{3}{2}x to get -\frac{33}{10}x.

$$1980-\frac{33}{10}x\geq 0$$

Subtract 1980 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{33}{10}x\geq -1980$$

Multiply both sides by -\frac{10}{33}, the reciprocal of -\frac{33}{10}. Since -\frac{33}{10} is negative, the inequality direction is changed.

$$x\leq -1980\left(-\frac{10}{33}\right)$$

Express -1980\left(-\frac{10}{33}\right) as a single fraction.

$$x\leq \frac{-1980\left(-10\right)}{33}$$

Multiply -1980 and -10 to get 19800.

$$x\leq \frac{19800}{33}$$

Divide 19800 by 33 to get 600.

$$x\leq 600$$