Please help solve for x
A.7^x+(4)(7^x) =245
B.x-|x+20=0
C.1+3/(x+1)=x
Simplify
D.(|24 +2|6 + |54 / |96 - |6
Keys: |=square root, /over or divided by
7^x + 4*7^x = 245
5*7^x = 245
7^x = 49
since 49 = 7^2, x=2
x-√x+20 = 0
think of this as
(√x)^2 - √x + 20 = 0
I think you must have a typo. It is much better if you have
(√x)^2 - √x - 20 = 0
(√x-5)(√x+4) = 0
√x = 5 or √x = -4
since √x is always positive, the only solution is
√x = 5
x = 25
1 + 3/(x+1) = x
(x+1) + 3 = x(x+1)
x^2-4 = 0
(x-2)(x+2) = 0
x = -2 or 2
Mismatched parentheses. I will assume you meant
(√24 + 2√6 + √54)/(√96 - √6)
If you factor out the perfect squares, you have
(2√6 + 2√6 + 3√6)/(4√6 - √6)
7√6 / 3√6
7/3
Thank you very much steve god bless you
Sure, I can help you solve these equations and simplify the expression. Let's go through them one by one:
A. 7^x+(4)(7^x) = 245
To solve for x in this equation, first notice that both terms on the left side have a common factor of 7^x. We can factor it out:
7^x(1 + 4) = 245
7^x(5) = 245
Now, divide both sides of the equation by 5 to isolate 7^x:
7^x = 245/5
7^x = 49
To find the value of x, take the logarithm (base 7) of both sides:
x = log₇(49)
Using the logarithmic property logₐ(b^c) = c * logₐ(b), we can rewrite the equation as:
x = log₇(7^2)
x = 2
So, the solution to A is x = 2.
B. x - |x+20|=0
To solve for x in this equation, let's consider the two cases where x is positive and x is negative:
Case 1: x ≥ 0
In this case, the absolute value expression can be simplified, and we have:
x - (x+20) = 0
x - x - 20 = 0
-20 = 0
Since there is no solution when -20 = 0, we can conclude that there are no solutions for this case.
Case 2: x < 0
In this case, the absolute value expression changes the sign, and we have:
x - (-x-20) = 0
x + x + 20 = 0
2x = -20
Divide both sides by 2:
x = -10
So, the solution to B is x = -10.
C. 1 + 3/(x+1) = x
To solve for x in this equation, let's isolate the x term on one side of the equation:
3/(x+1) = x - 1
To eliminate the fraction, we can multiply both sides by (x+1):
3 = (x+1)(x - 1)
Expand the right side:
3 = x² - 1
Rearrange the equation:
x² = 3 + 1
x² = 4
To solve for x, we take the square root of both sides:
x = ±√4
x = ±2
So, the solutions to C are x = 2 and x = -2.
D. (|24 +2|6 + |54 / |96 - |6
To simplify this expression, let's break it down step by step:
First, simplify the innermost absolute value terms:
|24 + 2| = |26| = 26
|96 - |6| = |96 - 6| = |90| = 90
Now we have:
(|26|6 + |54 / |90)
Next, divide 54 by 90:
54 / 90 = 3/5
Now we have:
(|26|6 + |3/5|)
Notice that there's another pair of absolute value signs. Since the value inside is positive, we can remove the outermost absolute value signs:
|26| = 26
Now we have:
(26*6 + |3/5|)
Multiplying 26 by 6 gives us:
156 + |3/5|
Since |3/5| is also positive, we can remove the absolute value signs:
|3/5| = 3/5
Finally, we have:
156 + 3/5
To combine the whole number and fraction, we need a common denominator:
156 = 156/1
Now, find the least common denominator which is 5:
156/1 = (5*156)/5 = 780/5
Now we have:
780/5 + 3/5
To add fractions, the denominators must be the same:
(780 + 3)/5
Now, perform the addition:
783/5
So, the simplified expression is 783/5.