Solve for x.
$\begin{array}{c}
8(4+2 x)=16 \\
x=[?]\end{array}$
Answer (2)
Divide both sides of the equation by 8: 4 + 2 x = 2 .
Subtract 4 from both sides: 2 x = − 2 .
Divide both sides by 2: x = − 1 .
The solution is − 1 .
Explanation
Understanding the Problem We are given the equation 8 ( 4 + 2 x ) = 16 and asked to solve for x . Our goal is to isolate x on one side of the equation.
Dividing by 8 First, we divide both sides of the equation by 8 to simplify it: 8 8 ( 4 + 2 x ) = 8 16 4 + 2 x = 2
Subtracting 4 Next, we subtract 4 from both sides of the equation to isolate the term with x :
4 + 2 x − 4 = 2 − 4 2 x = − 2
Dividing by 2 Finally, we divide both sides of the equation by 2 to solve for x :
2 2 x = 2 − 2 x = − 1
Final Answer Therefore, the solution to the equation is x = − 1 .
Examples
In real-world scenarios, solving linear equations like this can help determine unknown quantities. For example, if you know that buying a certain number of items, each costing a fixed amount plus an additional fee, results in a total cost, you can use a linear equation to find the cost of each item. Suppose a club charges $8 per ticket for an event, and after selling tickets to 4 members and some additional non-members (represented by 2x), the total revenue is $16. Solving the equation helps determine how many non-member tickets were sold.
The solution to the equation 8 ( 4 + 2 x ) = 16 is x = − 1 , found by distributing, isolating the variable, and dividing.
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