Solve the equation using the distributive property and properties of equality.
[tex]2(x-8)=68[/tex]
What is the value of [tex]x[/tex]?
A. 26
B. 30
C. 38
D. 42
Answer (2)
Apply the distributive property: 2 ( x − 8 ) → 2 x − 16 .
Add 16 to both sides of the equation: 2 x − 16 = 68 → 2 x = 84 .
Divide both sides by 2: 2 x = 84 → x = 42 .
The value of x is 42 .
Explanation
Understanding the Problem We are given the equation 2 ( x − 8 ) = 68 and we want to find the value of x using the distributive property and properties of equality.
Applying the Distributive Property First, we apply the distributive property to expand the left side of the equation. This means we multiply the 2 by both terms inside the parentheses: 2 × x − 2 × 8 = 68 .
Simplifying the Equation Now we simplify the equation: 2 x − 16 = 68 .
Adding to Both Sides Next, we want to isolate the term with x . To do this, we add 16 to both sides of the equation: 2 x − 16 + 16 = 68 + 16 .
Simplifying Again Simplifying again, we get 2 x = 84 .
Dividing to Solve for x Finally, to solve for x , we divide both sides of the equation by 2: 2 2 x = 2 84 .
Finding the Value of x This gives us x = 42 .
Examples
Imagine you're buying tickets for a group to an amusement park. Each ticket costs a certain amount, and there's a group discount. Using the distributive property helps you calculate the total cost efficiently. For example, if each ticket costs x dollars and there's a discount of 8 dollars per ticket, the total cost for 2 tickets can be represented as 2 ( x − 8 ) . If the total cost is 68 dollars, solving the equation 2 ( x − 8 ) = 68 tells you the original price of each ticket before the discount. This kind of problem-solving is useful in budgeting and making informed purchasing decisions.
By applying the distributive property to the equation 2(x - 8) = 68 and solving step-by-step, we find that x = 42. Therefore, the answer is option D.
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