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:
- \( x = 2 \) satisfies \( a = b \).
- \( x = 1 \) 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.