Question

Find the value of x in the expressions if A=3x+51
𝐴
=
3
𝑥
+
51
and B=6x−15
𝐵
=
6
𝑥
−
15
(1 point)

Answer 1

To find the value of \( x \) in the expressions \( A = 3x + 51 \) and \( B = 6x - 15 \), we can set the two expressions equal to each other if we are looking for a common value of \( A \) and \( B \):

\[
3x + 51 = 6x - 15
\]

Now, let's solve for \( x \):

1. Subtract \( 3x \) from both sides:

\[
51 = 6x - 3x - 15
\]

2. This simplifies to:

\[
51 = 3x - 15
\]

3. Next, add \( 15 \) to both sides:

\[
51 + 15 = 3x
\]

4. This simplifies to:

\[
66 = 3x
\]

5. Now, divide both sides by \( 3 \):

\[
x = \frac{66}{3} = 22
\]

Thus, the value of \( x \) is \( \boxed{22} \).

Answer 2

find the value of x in the expressions if
A = 3x + 51
B = 6x - 15
it is a triangle, and the other angle is 90 degrees.

Answer 3

To find the value of \( x \) for the expressions \( A = 3x + 51 \) and \( B = 6x - 15 \) in the context of a triangle where one angle is 90 degrees, you need to recognize that in a right triangle, the measures of the angles must add up to 180 degrees.

Assuming that \( A \) and \( B \) represent the measures of the two angles in the triangle along with the right angle, we can set up the following equation:

\[
A + B + 90 = 180
\]

This simplifies to:

\[
A + B = 90
\]

Now substitute the expressions for \( A \) and \( B \):

\[
(3x + 51) + (6x - 15) = 90
\]

Combine like terms:

\[
3x + 51 + 6x - 15 = 90
\]

\[
9x + 36 = 90
\]

Next, isolate \( 9x \) by subtracting 36 from both sides:

\[
9x = 90 - 36
\]

\[
9x = 54
\]

Now, divide both sides by 9:

\[
x = \frac{54}{9} = 6
\]

Thus, the value of \( x \) is \( \boxed{6} \).