Question

a=5x
b=2x+6
c=1x+7
find the value of x
x=

Answer 1

To find the value of \( x \), you need to set the equations \( a \), \( b \), and \( c \) equal to each other or find a relationship between them. Let's first equate \( a \) and \( b \) to see if we can solve for \( x \):

Set \( a = b \):
\[
5x = 2x + 6
\]
Subtract \( 2x \) from both sides:
\[
5x - 2x = 6
\]
\[
3x = 6
\]
Now, divide both sides by 3:
\[
x = 2
\]

Now let's check if this value of \( x \) also satisfies the other equations by substituting \( x = 2 \) back into the expressions for \( b \) and \( c \):

Calculate \( b \):
\[
b = 2(2) + 6 = 4 + 6 = 10
\]

Calculate \( c \):
\[
c = 1(2) + 7 = 2 + 7 = 9
\]

So, we have:
- \( a = 5(2) = 10 \)
- \( b = 10 \)
- \( c = 9 \)

Since \( a = b \) when \( x = 2 \), and \( c \) does not equal \( a \) or \( b\), this means \( x = 2 \) is a solution for \( a \) and \( b \), but we need to check if \( b \) and \( c \) can be equated or another form of solution is present.

Set \( b = c \):
\[
2x + 6 = 1x + 7
\]
Subtract \( 1x \) from both sides:
\[
2x - 1x = 7 - 6
\]
\[
x = 1
\]

Let's check \( x = 1 \) against the values of \( a \), \( b \), and \( c \):
- Calculate \( a \):
\[
a = 5(1) = 5
\]
- Calculate \( b \):
\[
b = 2(1) + 6 = 2 + 6 = 8
\]
- Calculate \( c \):
\[
c = 1(1) + 7 = 1 + 7 = 8
\]

With \( x = 1 \), we find \( b = c = 8 \), but \( a \neq b \): \( a = 5 \).

Hence, we found:
1. \( x = 2 \) satisfies \( a = b \).
2. \( x = 1 \) satisfies \( b = c \).

So, there are values \( x \) where specific pairs are equal. It's essential to clarify the conditions or relationships intended between \( a \), \( b \), and \( c \) to find the "common" value if required based on context.

If only one solution is to be provided based on which pair to equate, you can conclude:

\[
x = 2 \quad (for \, a = b)
\]

or
\[
x = 1 \quad (for \, b = c)
\]

Please clarify if you're looking for something specific.