Solve the following exercise:
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Solve the following exercise:
To open the parentheses on the left side, we'll use the formula:
We'll arrange the equation so that the terms with 'a' are on the right side, and maintain the plus and minus signs during the transfer:
Let's group the terms on the right side:
Let's divide both sides by 39:
Note that we can reduce the fraction since both numerator and denominator are divisible by 3:
\( \frac{-y}{5}=-25 \)
Many linear equations have fractional solutions! This is completely normal. The key is to simplify the fraction to its lowest terms, like reducing to .
When you see a negative number in front of parentheses, it multiplies every term inside. Think of -3(4a+8) as (-3)×(4a) + (-3)×(8) = -12a + (-24) = -12a - 24.
Either works! Choose the side that keeps your coefficient positive when possible. In this problem, moving a terms to the right gives 39a, which is easier than -39a.
Substitute back into the original equation. Calculate both sides: Left side: -3(4(-8/13)+8) = -72/13. Right side: 27(-8/13) = -216/13 = -72/13. They match!
Simplifying gives the cleanest form of your answer. and are equal, but the simplified version is easier to work with in future problems.
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