Solve the equation:
$\frac{2 w+1}{5}=rac{3}{8}$
The problem asks us to solve the linear equation \(\frac{2w+1}{5} = \frac{3}{8}\) for the variable \(w\). This is a simple equation involving a single variable, and we can solve it using standard algebraic techniques such as multiplication, subtraction, and division to isolate \(w\).
To solve for \(w\), we first clear the denominator on the left-hand side by multiplying both sides of the equation by \(5\):
\[ \frac{2w+1}{5} \times 5 = \frac{3}{8} \times 5 \]
\[ 2w + 1 = \frac{15}{8} \]
Next, we subtract \(1\) from both sides to isolate the term \(2w\):
\[ 2w = \frac{15}{8} - 1 \]
Since \(1 = \frac{8}{8}\), we can rewrite the right side as:
\[ 2w = \frac{15}{8} - \frac{8}{8} = \frac{7}{8} \]
Finally, we isolate \(w\) by dividing both sides of the equation by \(2\):
\[ w = \frac{7}{8} \div 2 \]
\[ w = \frac{7}{8} \times \frac{1}{2} = \frac{7}{16} \]
Thus, the value of \(w\) that satisfies the equation is \(\frac{7}{16}\).
Solving linear equations like this one is essential in many practical situations, such as when you need to calculate the correct dosage for a medication based on body weight, or when you are mixing ingredients for a recipe that needs to be scaled up or down. If a recipe calls for a ratio of 2 parts ingredient A plus a constant unit, and you need to match a specific final ratio of 3/8, you can use this algebraic method to find exactly how much ingredient A you need to add to your mixture.