Use the laws of exponents to solve for x in the equation 7294x−1=93x+8.(1 point)
Responses
x=196
x equals Start Fraction 19 over 6 End Fraction
x=9
x equals 9
x=−32
x equals negative Start Fraction 3 over 2 End Fraction
x=119
x equals Start Fraction 11 over 6 End Fraction
To solve the equation, we can start by rewriting the equation using the laws of exponents.
First, we can rewrite 729 as (3^6) and 93 as (3^2).
So the equation becomes: (3^6)(4x-1) = (3^2)(3^3)(x+8).
Next, we can simplify both sides by distributing the exponent.
On the left side: (3^6)(4x-1) = (3^2)(3^3)(x+8)
Simplifying, we get: 3^6 * 4x - 3^6 * 1 = 3^2 * 3^3 * x + 3^2 * 3^3 * 8
On the right side: (3^2)(3^3)(x+8) = 3^5 * 3 * (x+8)
Simplifying, we get: 3^5 * 3(x+8) = 3^5 * 3 * x + 3^5 * 3 * 8
Now, we can cancel out the exponents on both sides.
On the left side: 3^6 * 4x - 3^6 = 3^5 * 3 * x + 3^5 * 3 * 8
Simplifying, we get: 4x - 1 = 3 * x + 3 * 8
On the right side: 3^5 * 3(x+8) = 3^5 * 3 * x + 3^5 * 3 * 8
Simplifying, we get: 3^5 * 3(x+8) = 3^5 * 3 * x + 3^5 * 3 * 8
Now, we can simplify the equation further by combining like terms.
On the left side: 4x - 1 = 3x + 24
On the right side: 3(x+8) = 3x + 24
Now we have a simple linear equation. To solve for x, we can start by moving all terms with x to one side of the equation and moving constant terms to the other side.
On the left side: 4x - 1 - 3x = 3x + 24 - 3x
Simplifying, we get: x - 1 = 24
On the right side: 3(x+8) = 24 + 3x
Simplifying, we get: 3x + 24 = 24 + 3x
At this point, we can see that both sides of the equation are equal. This means that the equation has infinitely many solutions. Therefore, the correct answer is: x can be any real number.