Solve $10+6(-9-4 x)=10(x-12)+8$
A) $x=2$
B) $x=17$
C) $x=-18$
D) $x=-6$
Answer (2)
Expand both sides of the equation.
Combine like terms on both sides of the equation.
Isolate the variable x on one side of the equation.
Solve for x : x = 34 68 = 2 , so the final answer is 2 .
Explanation
Problem Analysis We are given the equation 10 + 6 ( − 9 − 4 x ) = 10 ( x − 12 ) + 8 and asked to solve for x . We will expand and simplify the equation to isolate x .
Expanding the equation First, distribute the constants on both sides of the equation: 10 − 54 − 24 x = 10 x − 120 + 8
Combining Like Terms Combine like terms on both sides: − 44 − 24 x = 10 x − 112
Isolating x Add 24 x to both sides: − 44 = 34 x − 112
Further isolating x Add 112 to both sides: 68 = 34 x
Solving for x Divide both sides by 34 :
x = 34 68 = 2
Final Answer Therefore, the solution is x = 2 .
Examples
Solving linear equations is a fundamental skill in algebra and has numerous real-world applications. For example, suppose you are planning a road trip and need to determine how much gasoline you need to purchase. If you know the distance of the trip, the fuel efficiency of your car, and the price of gasoline, you can set up a linear equation to calculate the total cost of the gasoline. Similarly, linear equations are used in budgeting, finance, and many other areas to model relationships between variables and make predictions.
The solution to the equation 10 + 6 ( − 9 − 4 x ) = 10 ( x − 12 ) + 8 is found by expanding, combining like terms, and isolating the variable. After working through the calculations, we determine that x = 2 . This corresponds to option A.
;
