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Solve for x

X+8/5=10-x and


Simplify

3(y+7)^5/(y+7)^4

User Akeem
by
8.2k points

1 Answer

3 votes

Final answer:

To solve the equation x + 8/5 = 10 - x, we rearrange to isolate x, yielding x = 21/5 or 4.2. To simplify the expression
3(y+7)^5/(y+7)^4, we subtract exponents and obtain the simplified form 3(y+7).

Step-by-step explanation:

Solving the Equation X+8/5=10-x

To solve the equation
x + (8)/(5) = 10 - x, we first want to get all the x terms on one side and the constants on the other. This can be achieved by adding x to both sides of the equation and subtracting \frac{8}{5} from both sides.

Doing this gives us:


2x = 10 - (8)/(5)

To simplify, we convert 10 to fifths. 10 is the same as
(50)/(5), so we have:


2x = (50)/(5) - (8)/(5)

Combining the fractions we get:


2x = (42)/(5)

Now, we divide both sides by 2 to solve for x:


x = (42)/(5) / 2


x = (21)/(5)

Thus, x equals
(21)/(5) or 4.2

Simplifying the Expression
3(y+7)^5/(y+7)^4

To simplify the expression
(3(y+7)^5)/((y+7)^4), we observe that the numerator and the denominator have a common base of (y + 7) raised to a power. We can apply the laws of exponents which state that when dividing like bases, we subtract the exponents. This gives us:


3(y+7)^(5-4)

Which simplifies further to:


3(y+7)

This is the simplified form of the expression.

User Babanana
by
7.7k points

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