1. Solve the equation below for x interms of a
4(ax+3)-3ax=25+3a
2. The formula for the sum of the degree measures of the interior angles of a polygon is S=180(n-2). Solve for n, the number of sides of the polygon, in terms of S.
IM STRUGGLING PLEASE HELP
1.
4 ( ax + 3 )-3 ax = 25 + 3a
4 * ax + 4 * 3 - 3 ax = 25 + 3a
4 ax + 12 - 3 ax = 25 + 3a
4 ax - 3 ax + 12 = 25 + 3a
ax + 12 = 25 + 3a Subtract 12 to both sides
ax + 12 - 12 = 25 + 3a - 12
ax = 25 - 12 + 3a
ax = 13 + 3a Subtract 3a to both sides
ax - 3a = 13 + 3a - 3a
ax - 3a = 13
a ( x - 3 ) = 13 Divide both sides by a
x - 3 = 13 / a Add 3 to both sides
x - 3 + 3 = 13 / a + 3
x = 13 / a + 3 = 13 / a + 3a / a
x = ( 13 + 3a ) / a
2.
S = 180 ( n - 2 ) Divide both sides by 180
S / 180 = n - 2 Add 2 to both sides
S / 180 + 2 = n - 2 + 2
S / 180 + 2 = n
n = S / 180 + 2
bosianian it said solve in terms of S
I solved it like:
S=180(n-2) Distribute 180
S=180n-360 Add 360
S+360=180n Divide by 180
S+2=n
Iām confused as to what I am doing wrong.
1. Sure, let's solve the equation using some mathematical clownery!
We have 4(ax + 3) - 3ax = 25 + 3a
Let's start by distributing 4 to the terms inside the parentheses:
4ax + 12 - 3ax = 25 + 3a
Combining like terms, we get:
ax + 12 = 25 + 3a
Now, let's isolate the terms with "x" on one side of the equation:
ax - 3a = 25 - 12
ax - 3a = 13
Finally, let's factor out the "x" on the left side of the equation:
x(a - 3) = 13
Now, to solve for x, we can divide both sides of the equation by (a - 3):
x = 13 / (a - 3)
And there you have it! The solution for x in terms of a is x = 13 / (a - 3).
2. Now let's move on to the second question!
The formula for the sum of the degree measures of the interior angles of a polygon is S = 180(n - 2). We need to solve for n in terms of S.
To do this, let's start by isolating the variable n.
S = 180(n - 2)
Distribute 180 to the terms inside the parentheses:
S = 180n - 360
Now, let's get rid of the -360 term by moving it to the other side:
S + 360 = 180n
To simplify further, let's divide both sides by 180:
(S + 360) / 180 = n
Simplifying that, we get:
n = (S + 360) / 180
And there you have it! The solution for n in terms of S is n = (S + 360) / 180.
Remember, even if math is confusing sometimes, laughter is always the best solution! Keep smiling!
Of course! I'll help you solve both equations step by step.
1. Solve the equation 4(ax+3)-3ax=25+3a for x in terms of a:
First, let's simplify the equation by expanding and combining like terms:
4(ax+3)-3ax=25+3a
4ax + 12 - 3ax = 25 + 3a
ax + 12 = 25 + 3a
Next, let's isolate the terms with x on one side of the equation:
ax - 3a = 25 - 12
ax - 3a = 13
Now, we can factor out the common variable, a, from the left side:
a(x - 3) = 13
Finally, we can solve for x by dividing both sides of the equation by a:
(x - 3) = 13/a
So, x in terms of a is:
x = 13/a + 3
2. Solve the equation S = 180(n-2) for n in terms of S:
To solve for n, we need to isolate it on one side of the equation. Let's go step by step:
S = 180(n-2)
First, distribute the 180 to both terms inside the parentheses:
S = 180n - 360
Next, let's isolate n by moving the constant term -360 to the other side of the equation:
S + 360 = 180n
To solve for n, we need to get rid of the coefficient 180. Divide both sides of the equation by 180:
(S + 360)/180 = (180n)/180
Simplifying further:
(S + 360)/180 = n
Now, we can simplify the equation:
n = (S + 360)/180
So, n in terms of S is:
n = (S + 360)/180
I hope this helps! Let me know if you have any further questions.
Where you got the s from ?
these just use the normal sequences of operations...
4(ax+3)-3ax=25+3a
4ax+12-3ax = 25+3a
ax+12 = 25+3a
ax-3a = 25-12
a(x-3) = 12
a = 13/(x-3)
S=180(n-2)
S = 180n-360
S+360 = 180n
n = (S+360)/180 = S/180 + 2