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)
By using the distributive property and properties of equality, we determined that the solution to the equation 2 ( x − 8 ) = 68 is x = 42 . Therefore, the correct answer is option D: 42.
;
Apply the distributive property: 2 ( x − 8 ) = 2 x − 16 .
Set up the equation: 2 x − 16 = 68 .
Add 16 to both sides: 2 x = 84 .
Divide by 2 to solve for x: x = 42 .
Explanation
Understanding the Problem We are given the equation 2 ( x − 8 ) = 68 and we need to solve for 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 Next, we simplify the equation: 2 x − 16 = 68 .
Adding 16 to Both Sides Now, 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 Further Simplifying both sides gives us: 2 x = 84 .
Dividing by 2 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 simplifies to x = 42 . Therefore, the value of x is 42.
Examples
Imagine you're buying tickets for a group to an amusement park. The total cost is $68, but there's a $2 discount on each ticket. If the equation 2 ( x − 8 ) = 68 represents this situation, where x is the original price of each ticket, solving for x tells you the original price before the discount. This kind of problem helps in budgeting and understanding costs in everyday scenarios.
