Question

3.11. clearing fractions
two notebook pages. you must write the original equation on your paper.
solve each equation by first clearing fractions (this must be shown in your work)
work must be shown going down under the original equation. each step is written under the previous step. each line may contain only one equal sign
you must show inverse operations on both sides of the equation
show all work! solutions only receive no credit

1. \\(\frac{x}{3} - \frac{1}{6} = \frac{1}{2}\\) 2. \\(\frac{6}{6}c + \frac{1}{2} = -\frac{2}{3}\\)
2. \\(\frac{1}{2}a - \frac{1}{4} = -\frac{3}{28}\\) 4. \\(-\frac{2}{3}y + 3 = \frac{1}{8}\\)
3. \\(\frac{4}{5} + \frac{1}{2}x = -1\\) 6. \\(x + \frac{2}{5} = -\frac{1}{3}\\)
4. \\(\frac{5}{6}x - 1 = \frac{1}{3}x + 7\\) 8. \\(5x - \frac{11}{8} = \frac{9}{8}x - \frac{21}{4}\\)
5. \\(\frac{7a}{6} - \frac{21}{40} = \frac{3}{8} + \frac{10a}{3}\\) 10. \\(-\frac{11}{6}y + \frac{13}{4} = -\frac{2}{5}y - \frac{5}{8}y\\)

Explanation:

Step1: Clear fractions (multiply by LCM)

The equation is $\frac{x}{3} - \frac{1}{6} = \frac{1}{2}$. The least common multiple (LCM) of 3, 6, and 2 is 6. Multiply each term by 6:
$6 \times \frac{x}{3} - 6 \times \frac{1}{6} = 6 \times \frac{1}{2}$
Simplify: $2x - 1 = 3$

Step2: Solve for x (add 1 to both sides)

Add 1 to both sides:
$2x - 1 + 1 = 3 + 1$
Simplify: $2x = 4$

Step3: Divide by 2 (isolate x)

Divide both sides by 2:
$\frac{2x}{2} = \frac{4}{2}$
Simplify: $x = 2$

Answer:

$x = 2$