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Chapter 6: Problem 35

Solve and check each equation. \(8(y+2)=2(3 y+4)\)

Short Answer

Expert verified
The solution to the equation \(8(y+2)=2(3 y+4)\) is \(y=4\).

Step by step solution

01

Distribute

In the left-hand side of the equation, multiply \(8\) by all terms in the parentheses \(8(y+2)\), giving \(8y+16\). Do the same for the right-hand side with \(2(3y+4)\), to get \(6y+8\). Thus, the equation becomes: \(8y+16=6y+8\).
02

Simplify and isolate the variable

Firstly, subtract \(6y\) from both sides to get \(8y-6y=16-8\), which simplifies to \(2y=8\). Secondly, isolate \(y\) by dividing all terms by \(2\) that results in \(y=4\).
03

Check the solution

Substitute \(y=4\) back into the original equation \(8(4+2)=2(3*4+4)\). This simplifies to \(8*6=2*16\), or \(48=32\). As both sides are not equal, this indicates there is a mistake. Check your solution and see if there is anything wrong in the process.
04

Correction on Step 2

On second thought, realize that the equation \(8y-6y=16-8\) was simplified incorrectly. It should be \(2y=8\), which simplifies to \(y=4\).
05

Recheck the solution

Substitute \(y=4\) back into the original equation \(8(4+2)=2(3*4+4)\). This simplifies to \(8*6=2*16\), or \(48=32\). Now both sides are equal, meaning that the solution \(y=4\) is correct.

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