Solve for y:
5((132 - 3y)/4) - 2y = -42
Answer (2)
To solve the equation, we first distribute and eliminate the fraction, leading to y = 36 . The steps involve combining like terms and isolating y . The final solution is determined through simple arithmetic.
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To solve the equation 5 ( 4 132 − 3 y ) − 2 y = − 42 , we will follow these steps to find the value of y :
Simplify Inside the Parentheses:
Start by distributing the 5 into the fraction:
5 × 4 132 − 3 y = 4 5 ( 132 − 3 y ) = 4 660 − 15 y
Rewrite the Equation:
Substitute back into the original equation:
4 660 − 15 y − 2 y = − 42
Eliminate the Fraction:
Multiply all terms by 4 to remove the fraction:
660 − 15 y − 8 y = − 168
Combine Like Terms:
Combine − 15 y and − 8 y :
660 − 23 y = − 168
Solve for y :
First, isolate the term with y by subtracting 660 from both sides:
− 23 y = − 168 − 660
− 23 y = − 828
Divide both sides by [tex]-23[/tex]:
\[y = \frac{-828}{-23}\]
y = 36
Verify the Solution:
Substitute y = 36 back into the original equation to check:
[ 5\left(\frac{132 - 3(36)}{4}\right) - 2(36)
= 5\left(\frac{132 - 108}{4}\right) - 72 = 5\left(\frac{24}{4}\right) - 72 = 5 \times 6 - 72 = 30 - 72 = -42 ]
Since both sides of the equation are equal, y = 36 is the correct solution.
Therefore, the solution to the equation is y = 36 .
