Question 1

What is the least common denominator (LCD) of the fractions $$\frac{5}{6}$$, $$\frac{3}{7}$$, and $$\frac{x}{42}$$?

Accepted Answer

$$42$$

Question 2

After multiplying both sides of the inequality $$\frac{5}{6} + \frac{3}{7} \leq \frac{x}{42} by $$the LCD, what is the resulting equation?

Accepted Answer

Question 3

What is the solution set for the inequality $$\frac{5}{6} + \frac{3}{7} \leq \frac{x}{42}$$ after clearing fractions and solving for $$x$$?

Accepted Answer

$$(-\infty, 53]$$

Question 4

Which property is used when multiplying both sides of an inequality by the LCD to clear fractions?

Accepted Answer

Multiplicative property of equality

Question 5

If you have the inequality $$\frac{a}{b} + \frac{c}{d} \leq \frac{e}{f}$$, what is the first step to solve it?

Accepted Answer

Find the least common denominator (LCD) of $$b$$, $$d$$, and $$f$$

Question 6

A medical dosage calculation requires solving $$\frac{2}{5} + \frac{1}{4} \leq \frac{x}{20}. $$What is the LCD?

Accepted Answer

$$20$$

Question 7

After clearing fractions in $$\frac{2}{5} + \frac{1}{4} \leq \frac{x}{20}$$, what is the resulting inequality?

Accepted Answer

Question 8

In a real-world scenario, a chemical reaction requires $$\frac{3}{8}$$ liters of solution A and $$\frac{1}{2}$$ liters of solution B. If the total must not exceed $$\frac{x}{16}$$ liters, what is the LCD?

Accepted Answer

$$16$$

Question 9

What is the solution set for $$\frac{3}{8} + \frac{1}{2} \leq \frac{x}{16}$$ after clearing fractions and solving for $$x$$?

Accepted Answer

$$(-\infty, 14]$$

Question 10

Which step is necessary to eliminate fractions in an inequality before solving for the variable?

Accepted Answer

Multiply both sides by the LCD

Question 11

If you have $$\frac{4}{9} + \frac{2}{3} \leq \frac{x}{18}$$, what is the correct solution set for $$x$$?

Accepted Answer

$$(-\infty, 12]$$

Question 12

Why is it important to use the LCD when solving inequalities with fractions?

Accepted Answer

It eliminates all denominators, simplifying the equation

Question 13

A historical event required $$\frac{1}{3} of a $$resource from one country and $$\frac{1}{4}$$ from another. If the total must not exceed $$\frac{x}{12}$$, what is the solution set for $$x$$?

Accepted Answer

$$(-\infty, 7]$$

Question 14

What is the result of applying the distributive property to $$42 \left( \frac{5}{6} + \frac{3}{7} \right)$$?

Accepted Answer

$$35 + 18$$

Question 15

If a recipe requires $$\frac{1}{5}$$ cup of sugar and $$\frac{2}{3}$$ cup of flour, and the total must not exceed $$\frac{x}{15}$$ cups, what is the LCD?

Accepted Answer

$$15$$

Question 16

After clearing fractions in $$\frac{1}{5} + \frac{2}{3} \leq \frac{x}{15}$$, what is the solution set for $$x$$?

Accepted Answer

$$(-\infty, 11]$$

Question 17

Which of the following is a common mistake when solving inequalities with fractions?

Accepted Answer

Multiplying only one side by the LCD

Question 18

In solving $$\frac{5}{6} + \frac{3}{7} \leq \frac{x}{42}$$, what is the value of $$35 + 18$$?

Accepted Answer

$$53$$

Question 19

If you solve $$\frac{a}{b} + \frac{c}{d} \leq \frac{x}{f}$$ and get $$m \leq x$$, what is the solution set?

Accepted Answer

$$(-\infty, m]$$

Solving Fractional Inequalities Using the Least Common Denominator

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