How to solve the equation 9v = 8 + v

1 answer:

5 0

Here are some things you should know when solving algebraic equations.

If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.

You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.

To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.

The distributive property is another important rule you will need to understand.

The distributive property is used mostly for simplifying parentheses in expressions/equations.

For example, how would you get rid of the parentheses here?

6(x + 1)

If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac

So, now we can simplify our expression.

6(x + 1) = 6x + 6

Now let's solve your equation.

9v = 8 + v
8v = 8 <-- Subtract v from each side
v = 1 <-- Divide both sides by 8

So, v is equal to 1.

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What is the degree of the polynomial 5x^2y^2 + 4y^3 + 3x + 10

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Recall that for y2, y is the base and 2 is the exponent.

More examples showing how to find the degree of a polynomial.

Example #1: 4x2 + 6x + 5

This polynomial has three terms. The first one is 4x2, the second is 6x, and the third is 5.

The exponent of the first term is 2.

The exponent of the second term is 1 because 6x = 6x^1.

The exponent of the third term is 0 because 5 = 5x^0.

What? 5x^0 = 5?

Well, anything with an exponent of 0 is always equal to 1.

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