What is the solution for $x$ in the equation?
$-3 x+7 x-8=34+9 x-2$
A. $x=8$
B. $x=\frac{1}{8}$
C. $x=-8$
D. $x=-\frac{1}{8}$
Answer (1)
Combine like terms on both sides of the equation: 4 x − 8 = 32 + 9 x .
Isolate the x terms on one side: − 8 = 32 + 5 x .
Isolate the constant terms on the other side: − 40 = 5 x .
Solve for x: x = 5 − 40 = − 8 . The solution is − 8 .
Explanation
Simplify the equation We are given the equation − 3 x + 7 x − 8 = 34 + 9 x − 2 . Our goal is to solve for x . First, we simplify both sides of the equation by combining like terms.
Combine like terms On the left side, we have − 3 x + 7 x = 4 x . So the left side becomes 4 x − 8 . On the right side, we have 34 − 2 = 32 . So the right side becomes 32 + 9 x . Now our equation is 4 x − 8 = 32 + 9 x .
Isolate x terms Next, we want to isolate the x terms on one side of the equation and the constant terms on the other side. We can subtract 4 x from both sides to get − 8 = 32 + 5 x .
Isolate constant terms Now, subtract 32 from both sides to isolate the x term: − 8 − 32 = 5 x , which simplifies to − 40 = 5 x .
Solve for x Finally, divide both sides by 5 to solve for x : x = 5 − 40 = − 8 .
Final Answer Therefore, the solution for x is − 8 .
Examples
In physics, this type of equation can be used to model the motion of an object under constant acceleration. For example, if the position of an object at time t is given by x ( t ) = − 3 t + 7 t − 8 , and we want to find the time t when the object's position is 34 + 9 t − 2 , we would solve the equation − 3 t + 7 t − 8 = 34 + 9 t − 2 for t . This helps us understand and predict the object's behavior.
