Solve the equation for the given variable. If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal. $$ 6(2 y-3)+14=2(4 y+1)+23 $$ One solution, and $$ y= $$ No solution Infinite number of solutions

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UpStudy AI · Accepted Answer

1. Expand both sides of the equation:
   - Left-hand side:  
     $$
     6(2y-3)+14 = 12y - 18 + 14 = 12y - 4
     $$
   - Right-hand side:  
     $$
     2(4y+1)+23 = 8y + 2 + 23 = 8y + 25
     $$

2. Set the equation:
   $$
   12y - 4 = 8y + 25
   $$

3. Isolate the variable $$y$$:
   $$
   12y - 8y - 4 = 25 \quad \Rightarrow \quad 4y - 4 = 25
   $$

4. Add 4 to both sides:
   $$
   4y = 29
   $$

5. Divide both sides by 4:
   $$
   y = \frac{29}{4}
   $$

One solution, and $$y = \frac{29}{4}$$.
$$ y = \frac{29}{4} $$

Solve the equation for the given variable. If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal. \( 6(2 y-3)+14=2(4 y+1)+23 \) One solution, and \( y= \) No solution Infinite number of solutions

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