Question

write down the equation and solve it. use a lcd to eliminate the fraction.\\(\frac{2}{3}x + 7 + \frac{1}{6}x = 12\\)\\(\square\\) \\(x = 6\\)\\(\square\\) \\(x = -6\\)\\(\square\\) \\(x = 5\\)\\(\square\\) \\(x = 4\\)\\(\text{rewatch}\\)\\(\text{submit}\\)

Explanation:

Step1: Find the LCD of 3 and 6

The denominators are 3 and 6. The least common denominator (LCD) of 3 and 6 is 6.

Step2: Multiply each term by 6 to eliminate fractions

Multiply each term in the equation \(\frac{2}{3}x + 7 + \frac{1}{6}x = 12\) by 6:
\(6\times\frac{2}{3}x + 6\times7 + 6\times\frac{1}{6}x = 6\times12\)
Simplify each term:
\(4x + 42 + x = 72\)

Step3: Combine like terms

Combine the \(x\)-terms: \(4x + x + 42 = 72\)
\(5x + 42 = 72\)

Step4: Subtract 42 from both sides

\(5x + 42 - 42 = 72 - 42\)
\(5x = 30\)

Step5: Divide both sides by 5

\(\frac{5x}{5} = \frac{30}{5}\)
\(x = 6\)

Answer:

x = 6