Select the correct answer.
Which value of $w$ makes this equation true?
[tex]\frac{5 w+4}{3}=\frac{3 w}{2}[/tex]
A. -8
B. -2
C. -1
D. 8
Answer (2)
Multiply both sides of the equation by 6 to eliminate the fractions: 2 ( 5 w + 4 ) = 3 ( 3 w ) .
Expand both sides: 10 w + 8 = 9 w .
Subtract 9 w from both sides: w + 8 = 0 .
Solve for w : w = − 8 . The correct answer is − 8 .
Explanation
Problem Analysis We are given the equation 3 5 w + 4 = 2 3 w and asked to find the value of w that makes the equation true. We can solve this equation by first eliminating the fractions.
Eliminating Fractions To eliminate the fractions, we multiply both sides of the equation by the least common multiple of the denominators, which is 6. This gives us: 6 × 3 5 w + 4 = 6 × 2 3 w Simplifying, we get: 2 ( 5 w + 4 ) = 3 ( 3 w )
Expanding the Equation Next, we expand both sides of the equation: 10 w + 8 = 9 w
Isolating w Now, we want to isolate w . We can subtract 9 w from both sides of the equation: 10 w − 9 w + 8 = 9 w − 9 w w + 8 = 0
Solving for w Finally, we subtract 8 from both sides to solve for w :
w + 8 − 8 = 0 − 8 w = − 8 So the value of w that makes the equation true is -8.
Checking the Answer We can check our answer by substituting w = − 8 into the original equation: 3 5 ( − 8 ) + 4 = 2 3 ( − 8 ) 3 − 40 + 4 = 2 − 24 3 − 36 = − 12 − 12 = − 12 Since the equation holds true, our answer is correct.
Examples
In electrical engineering, you might use similar equations to calculate the current in a circuit with resistors connected in a specific way. The variable 'w' could represent the current, and the fractions represent the resistance ratios. Solving for 'w' helps determine the current flow in the circuit, which is crucial for designing and analyzing electrical systems.
The value of w that makes the equation 3 5 w + 4 = 2 3 w true is − 8 .
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