Question

question 6 of 34 step 1 of 1 solve the following linear equation. \\(\frac{2y - 7}{3} + \frac{15}{6} = \frac{4y + 1}{6}\\) answer 2 points selecting an option will display any text boxes needed to complete your answer. \\(\square\\) no solution (\\(\emptyset\\)) \\(\bigcirc\\) one solution \\(\bigcirc\\) infinite solutions (\\(\mathbb{r}\\)) keyboard shortcuts

Explanation:

Step1: Eliminate denominators

Multiply each term by 6 (LCM of 3 and 6) to get rid of fractions:
$6\times\frac{2y - 7}{3}+6\times\frac{15}{6}=6\times\frac{4y + 1}{6}$
Simplify: $2(2y - 7)+15 = 4y + 1$

Step2: Expand and simplify

Expand $2(2y - 7)$: $4y - 14 + 15 = 4y + 1$
Combine like terms: $4y + 1 = 4y + 1$

Step3: Analyze the equation

Subtract $4y$ from both sides: $1 = 1$.
This is a true statement, meaning the equation holds for all real $y$.

Answer:

Infinite Solutions ($\mathbb{R}$)