Solve for $q$. \n$\frac{2}{2 q+3}=\frac{1}{8}$
Answer (1)
Multiply both sides by 8 ( 2 q + 3 ) to eliminate fractions: 16 = 2 q + 3 .
Subtract 3 from both sides: 13 = 2 q .
Divide both sides by 2 to solve for q : q = 2 13 .
The solution is 2 13 .
Explanation
Problem Analysis We are given the equation 2 q + 3 2 = 8 1 and our goal is to solve for q .
Eliminating Fractions To eliminate the fractions, we can multiply both sides of the equation by 8 ( 2 q + 3 ) . This gives us: 8 ( 2 q + 3 ) ⋅ 2 q + 3 2 = 8 ( 2 q + 3 ) ⋅ 8 1 Simplifying, we get: 8 ⋅ 2 = 2 q + 3 16 = 2 q + 3
Isolating the Term with q Now, we want to isolate the term with q . To do this, we subtract 3 from both sides of the equation: 16 − 3 = 2 q + 3 − 3 13 = 2 q
Solving for q Finally, to solve for q , we divide both sides of the equation by 2: 2 13 = 2 2 q q = 2 13 So, q = 2 13 or q = 6.5 .
Verification To verify our solution, we substitute q = 2 13 back into the original equation: 2 ( 2 13 ) + 3 2 = 13 + 3 2 = 16 2 = 8 1 This confirms that our solution is correct.
Examples
Imagine you're baking a cake and need to adjust a recipe. If the original recipe calls for a certain amount of sugar relative to the flour, and you want to scale the recipe up or down, you'll need to solve an equation similar to this one to find the new amount of sugar needed. This type of problem helps in adjusting proportions accurately in various real-life situations, from cooking to mixing chemicals in a lab.
