What is the solution to this equation?
$7 x-2(x-10)=40$
A. $x=10$
B. $x=6$
C. $x=12$
D. $x=4
Answer (2)
Distribute the -2: 7 x − 2 x + 20 = 40 .
Combine like terms: 5 x + 20 = 40 .
Subtract 20 from both sides: 5 x = 20 .
Divide by 5 to find the solution: x = 4 , so the answer is 4 .
Explanation
Understanding the Problem We are given the equation 7 x − 2 ( x − 10 ) = 40 and we need to find the value of x that satisfies this equation.
Distributing the Parenthesis First, distribute the − 2 into the parenthesis: 7 x − 2 ( x − 10 ) = 7 x − 2 x + 20
Substituting Back into the Equation Now, substitute this back into the original equation: 7 x − 2 x + 20 = 40
Combining Like Terms Combine the like terms 7 x and − 2 x :
5 x + 20 = 40
Isolating the x Term Subtract 20 from both sides of the equation to isolate the term with x :
5 x + 20 − 20 = 40 − 20
5 x = 20
Solving for x Divide both sides by 5 to solve for x :
5 5 x = 5 20 x = 4
Final Answer Therefore, the solution to the equation is x = 4 .
Examples
Imagine you're buying concert tickets online. The base price is the same for everyone, but there's a discount for members. This equation is like figuring out the original price of the ticket if you know the discounted price and the membership discount. By solving for 'x', you find the initial cost before any reductions, helping you understand the true value and savings.
The solution to the equation 7 x − 2 ( x − 10 ) = 40 is x = 4 . This is obtained by distributing, combining like terms, isolating the variable, and solving for x . The correct answer choice is D, which corresponds to x = 4 .
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