To find the value of [tex]\( x \)[/tex], we need to solve the system of equations given:
[tex]\[ m<1 = 2x + 10 \][/tex]
[tex]\[ m<2 = 3x - 6 \][/tex]
Since [tex]\( m<1 \)[/tex] and [tex]\( m<2 \)[/tex] are stated to be equal, we set the equations equal to each other:
[tex]\[ 2x + 10 = 3x - 6 \][/tex]
Next, we solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex] on one side of the equation.
1. Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ 2x + 10 - 2x = 3x - 6 - 2x \][/tex]
Simplifies to:
[tex]\[ 10 = x - 6 \][/tex]
2. Add 6 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ 10 + 6 = x - 6 + 6 \][/tex]
Simplifies to:
[tex]\[ 16 = x \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{16} \)[/tex].
