# Answer: Solving Algebra Problems: du=-30x^2dx to x^2 dx = -(1/30)du

• MHB
• student231
In summary, the given equation is a representation of solving an algebra problem using the substitution method. This method involves replacing one variable with an equivalent expression to simplify the equation and solve for the unknown variable. The substitution method is necessary in this equation because it has two variables, making it difficult to solve using traditional techniques. The coefficient in front of the variables indicates the rate of change or slope of the equation, and it is important to consider when solving algebra problems. To check the solution, one can plug in the value of the unknown variable or use a graphing calculator.
student231
Hello,

Having a lapse in memory how was this 1) changed into 2) algebraically

1) du=-30x^2dx

2) x^2 dx = -(1/30)du thank you for any help.

student231 said:
Hello,

Having a lapse in memory how was this 1) changed into 2) algebraically

1) du=-30x^2dx

2) x^2 dx = -(1/30)du thank you for any help.

It appears both sides were divided by -30, or equivalently, multiplied by $$\displaystyle -\frac{1}{30}$$, and then arranged as shown. Does that make sense?

## What does the given equation mean?

The given equation, du=-30x^2dx to x^2 dx = -(1/30)du, is a mathematical representation of solving an algebra problem. It involves the use of the substitution method to simplify the equation and solve for the unknown variable, x.

## What is the substitution method in algebra?

The substitution method is a technique used in algebra to solve equations with multiple variables. It involves replacing one variable with an equivalent expression in terms of the other variable, which simplifies the equation and makes it easier to solve.

## Why is it necessary to use the substitution method in this equation?

In this equation, there are two variables, du and dx, which makes it difficult to solve using traditional algebraic techniques. The substitution method allows us to replace one of the variables with an equivalent expression, making it easier to solve for the unknown variable.

## What is the purpose of the coefficient in front of the variables?

The coefficient, -30, in front of the variables indicates the rate of change or the slope of the equation. It is important to consider the coefficient when solving algebra problems as it affects the final solution.

## How can I check my solution for this equation?

To check your solution for this equation, you can plug in the value of the unknown variable, x, into the original equation and see if it satisfies the equation. You can also use a graphing calculator to plot the original equation and your solution to see if they intersect at the same point.

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