Solve the following formula for $x$
$ y=7 m x-6 b $
$ x=\square$
Enter your answer as an expression.
But be careful...to enter an expression like $\frac{a+b}{3+m}$ you need to type $( a + b ) /(3+ m )$. You need parentheses for both the numerator and denominator.
Answer (2)
Add 6 b to both sides of the equation: y + 6 b = 7 m x .
Divide both sides by 7 m : 7 m y + 6 b = x .
Simplify to find x = 7 m y + 6 b .
The solution for x is: ( 7 m ) ( y + 6 b )
Explanation
Understanding the Problem We are given the equation y = 7 m x − 6 b and asked to solve for x . This involves isolating x on one side of the equation.
Isolating the term with x First, we add 6 b to both sides of the equation to get rid of the − 6 b term on the right side: y + 6 b = 7 m x − 6 b + 6 b y + 6 b = 7 m x
Solving for x Next, we divide both sides of the equation by 7 m to isolate x :
7 m y + 6 b = 7 m 7 m x 7 m y + 6 b = x
Final Answer Therefore, the solution for x is: x = 7 m y + 6 b
Examples
In physics, this type of equation can represent a linear relationship between variables, where solving for one variable in terms of others is crucial. For example, if y represents the final velocity of an object, x represents time, m is the acceleration, and b is a constant related to initial conditions, then solving for x allows you to determine the time it takes to reach a certain velocity given the acceleration and initial conditions. This is a fundamental concept in kinematics, helping to predict and analyze motion.
To solve for x in the equation y = 7 m x − 6 b , first add 6 b to both sides and then divide by 7 m . The final expression for x is x = ( 7 m ) ( y + 6 b ) .
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