Solve $-4 x+2(5 x-6)+2 x=44$ for $x$
A. $x=-9$
B. $x=-5$
C. $x=7$
D. $x=12
Answer (2)
Distribute the 2 in the term 2 ( 5 x − 6 ) : − 4 x + 10 x − 12 + 2 x = 44 .
Combine like terms: 8 x − 12 = 44 .
Add 12 to both sides: 8 x = 56 .
Divide by 8 : x = 7 . The solution is 7 .
Explanation
Problem Analysis We are given the equation − 4 x + 2 ( 5 x − 6 ) + 2 x = 44 and asked to solve for x . We will simplify the equation by distributing and combining like terms, then isolate x to find its value.
Distribute First, distribute the 2 in the term 2 ( 5 x − 6 ) : − 4 x + 10 x − 12 + 2 x = 44
Combine Like Terms Next, combine like terms on the left side of the equation: ( − 4 x + 10 x + 2 x ) − 12 = 44 8 x − 12 = 44
Isolate x Now, isolate the term with x by adding 12 to both sides of the equation: 8 x − 12 + 12 = 44 + 12 8 x = 56
Solve for x Finally, solve for x by dividing both sides of the equation by 8 :
8 8 x = 8 56 x = 7
Verify Solution To verify the solution, substitute x = 7 back into the original equation: − 4 ( 7 ) + 2 ( 5 ( 7 ) − 6 ) + 2 ( 7 ) = 44 − 28 + 2 ( 35 − 6 ) + 14 = 44 − 28 + 2 ( 29 ) + 14 = 44 − 28 + 58 + 14 = 44 30 + 14 = 44 44 = 44 The solution is correct.
Final Answer The solution to the equation − 4 x + 2 ( 5 x − 6 ) + 2 x = 44 is x = 7 .
Examples
Imagine you are managing a small business and need to calculate your break-even point. The equation above is a simplified model of how costs and revenues interact. By solving for x , you determine the number of units you need to sell to cover your fixed costs and start making a profit. This type of algebraic problem is fundamental in business planning and financial analysis.
The solution to the equation − 4 x + 2 ( 5 x − 6 ) + 2 x = 44 is x = 7 . This can be validated by substituting x = 7 back into the equation, confirming it holds true. Therefore, the correct answer is option C.
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