Solve 24x-1/25-5-x/2leq0.03002/0.03

$$\frac { 24 x - 1 } { 25 } - \frac { 5 - x } { 2 } \leq \frac { 0.03002 } { 0.03 }$$

Solve for x

$$x\leq \frac{5311}{2190}$$

Solution Steps

Multiply both sides of the equation by 50, the least common multiple of 25,2. Since 50 is positive, the inequality direction remains the same.

$$2\left(24x-1\right)-25\left(5-x\right)\leq 50\times \frac{0.03002}{0.03}$$

Use the distributive property to multiply 2 by 24x-1.

$$48x-2-25\left(5-x\right)\leq 50\times \frac{0.03002}{0.03}$$

Use the distributive property to multiply -25 by 5-x.

$$48x-2-125+25x\leq 50\times \frac{0.03002}{0.03}$$

Subtract 125 from -2 to get -127.

$$48x-127+25x\leq 50\times \frac{0.03002}{0.03}$$

Combine 48x and 25x to get 73x.

$$73x-127\leq 50\times \frac{0.03002}{0.03}$$

Expand \frac{0.03002}{0.03} by multiplying both numerator and the denominator by 100000.

$$73x-127\leq 50\times \frac{3002}{3000}$$

Reduce the fraction \frac{3002}{3000} to lowest terms by extracting and canceling out 2.

$$73x-127\leq 50\times \frac{1501}{1500}$$

Express 50\times \frac{1501}{1500} as a single fraction.

$$73x-127\leq \frac{50\times 1501}{1500}$$

Multiply 50 and 1501 to get 75050.

$$73x-127\leq \frac{75050}{1500}$$

Reduce the fraction \frac{75050}{1500} to lowest terms by extracting and canceling out 50.

$$73x-127\leq \frac{1501}{30}$$

Add 127 to both sides.

$$73x\leq \frac{1501}{30}+127$$

Convert 127 to fraction \frac{3810}{30}.

$$73x\leq \frac{1501}{30}+\frac{3810}{30}$$

Since \frac{1501}{30} and \frac{3810}{30} have the same denominator, add them by adding their numerators.

$$73x\leq \frac{1501+3810}{30}$$

Add 1501 and 3810 to get 5311.

$$73x\leq \frac{5311}{30}$$

Divide both sides by 73. Since 73 is positive, the inequality direction remains the same.

$$x\leq \frac{\frac{5311}{30}}{73}$$

Express \frac{\frac{5311}{30}}{73} as a single fraction.

$$x\leq \frac{5311}{30\times 73}$$

Multiply 30 and 73 to get 2190.

$$x\leq \frac{5311}{2190}$$