Answer :
To understand how the value of the expression [tex]\( m(x+6) \)[/tex] changes when the value of [tex]\( x \)[/tex] decreases by 4, let's analyze the situation step-by-step.
1. Original Expression:
[tex]\[ m(x + 6) \][/tex]
2. Decrease in x:
Let's denote the original value of [tex]\( x \)[/tex] by [tex]\( x \)[/tex]. If [tex]\( x \)[/tex] decreases by 4, the new value of [tex]\( x \)[/tex] becomes:
[tex]\[ x - 4 \][/tex]
3. New Expression:
Substitute [tex]\( x - 4 \)[/tex] into the original expression:
[tex]\[ m((x - 4) + 6) \][/tex]
4. Simplify the New Expression:
Simplify the expression inside the parentheses:
[tex]\[ m(x - 4 + 6) = m(x + 2) \][/tex]
5. Determine the Change in the Expression:
The original expression was [tex]\( m(x + 6) \)[/tex]. The new expression is [tex]\( m(x + 2) \)[/tex]. To find the change, we subtract the new expression from the original expression:
[tex]\[ m(x + 6) - m(x + 2) \][/tex]
Factor out the common factor [tex]\( m \)[/tex]:
[tex]\[ m[(x + 6) - (x + 2)] = m(x + 6 - x - 2) \][/tex]
[tex]\[ = m[6 - 2] \][/tex]
[tex]\[ = m \cdot 4 \][/tex]
6. Change in the Expression:
Therefore, the change in the expression is [tex]\( -4m \)[/tex], which means the value of [tex]\( m(x+6) \)[/tex] decreases by [tex]\( 4m \)[/tex] when [tex]\( x \)[/tex] decreases by 4.
Option B: It decreases by [tex]\( 4m \)[/tex].
So, the correct answer is: B
1. Original Expression:
[tex]\[ m(x + 6) \][/tex]
2. Decrease in x:
Let's denote the original value of [tex]\( x \)[/tex] by [tex]\( x \)[/tex]. If [tex]\( x \)[/tex] decreases by 4, the new value of [tex]\( x \)[/tex] becomes:
[tex]\[ x - 4 \][/tex]
3. New Expression:
Substitute [tex]\( x - 4 \)[/tex] into the original expression:
[tex]\[ m((x - 4) + 6) \][/tex]
4. Simplify the New Expression:
Simplify the expression inside the parentheses:
[tex]\[ m(x - 4 + 6) = m(x + 2) \][/tex]
5. Determine the Change in the Expression:
The original expression was [tex]\( m(x + 6) \)[/tex]. The new expression is [tex]\( m(x + 2) \)[/tex]. To find the change, we subtract the new expression from the original expression:
[tex]\[ m(x + 6) - m(x + 2) \][/tex]
Factor out the common factor [tex]\( m \)[/tex]:
[tex]\[ m[(x + 6) - (x + 2)] = m(x + 6 - x - 2) \][/tex]
[tex]\[ = m[6 - 2] \][/tex]
[tex]\[ = m \cdot 4 \][/tex]
6. Change in the Expression:
Therefore, the change in the expression is [tex]\( -4m \)[/tex], which means the value of [tex]\( m(x+6) \)[/tex] decreases by [tex]\( 4m \)[/tex] when [tex]\( x \)[/tex] decreases by 4.
Option B: It decreases by [tex]\( 4m \)[/tex].
So, the correct answer is: B
