Answer :
Let's analyze the expression [tex]\( m(x + 9) \)[/tex] and see how it changes when the value of [tex]\( x \)[/tex] decreases by 6.
1. Initial Expression: The initial expression provided is [tex]\( m(x + 9) \)[/tex].
2. Change in [tex]\( x \)[/tex]: If [tex]\( x \)[/tex] decreases by 6, we can express the new value of [tex]\( x \)[/tex] as [tex]\( x - 6 \)[/tex].
3. Substitute the New Value of [tex]\( x \)[/tex]: Substitute [tex]\( x - 6 \)[/tex] in place of [tex]\( x \)[/tex] in the initial expression:
[tex]\[ m((x - 6) + 9) \][/tex]
4. Simplify the Expression: Simplify the expression inside the parentheses:
[tex]\[ m(x - 6 + 9) = m(x + 3) \][/tex]
5. Compare the Expressions: Now, we need to compare the new expression [tex]\( m(x + 3) \)[/tex] with the initial expression [tex]\( m(x + 9) \)[/tex]. We want to determine how the value changes:
[tex]\[ m(x + 3) - m(x + 9) \][/tex]
6. Simplify the Comparison: Simplify the difference between the two expressions:
[tex]\[ m(x + 3) - m(x + 9) = m(x + 3) - m(x + 9) = m[(x + 3) - (x + 9)] \][/tex]
7. Calculate Inside the Parentheses: Perform the subtraction inside the parentheses:
[tex]\[ m[(x + 3) - (x + 9)] = m[x + 3 - x - 9] = m[3 - 9] = m(-6) \][/tex]
8. Simplify Further: The term [tex]\( m(-6) \)[/tex] simplifies to:
[tex]\[ m(-6) = -6m \][/tex]
Thus, when the value of [tex]\( x \)[/tex] decreases by 6, the expression [tex]\( m(x + 9) \)[/tex] decreases by [tex]\( 6m \)[/tex].
So, the correct answer is:
B. It decreases by 6m.
1. Initial Expression: The initial expression provided is [tex]\( m(x + 9) \)[/tex].
2. Change in [tex]\( x \)[/tex]: If [tex]\( x \)[/tex] decreases by 6, we can express the new value of [tex]\( x \)[/tex] as [tex]\( x - 6 \)[/tex].
3. Substitute the New Value of [tex]\( x \)[/tex]: Substitute [tex]\( x - 6 \)[/tex] in place of [tex]\( x \)[/tex] in the initial expression:
[tex]\[ m((x - 6) + 9) \][/tex]
4. Simplify the Expression: Simplify the expression inside the parentheses:
[tex]\[ m(x - 6 + 9) = m(x + 3) \][/tex]
5. Compare the Expressions: Now, we need to compare the new expression [tex]\( m(x + 3) \)[/tex] with the initial expression [tex]\( m(x + 9) \)[/tex]. We want to determine how the value changes:
[tex]\[ m(x + 3) - m(x + 9) \][/tex]
6. Simplify the Comparison: Simplify the difference between the two expressions:
[tex]\[ m(x + 3) - m(x + 9) = m(x + 3) - m(x + 9) = m[(x + 3) - (x + 9)] \][/tex]
7. Calculate Inside the Parentheses: Perform the subtraction inside the parentheses:
[tex]\[ m[(x + 3) - (x + 9)] = m[x + 3 - x - 9] = m[3 - 9] = m(-6) \][/tex]
8. Simplify Further: The term [tex]\( m(-6) \)[/tex] simplifies to:
[tex]\[ m(-6) = -6m \][/tex]
Thus, when the value of [tex]\( x \)[/tex] decreases by 6, the expression [tex]\( m(x + 9) \)[/tex] decreases by [tex]\( 6m \)[/tex].
So, the correct answer is:
B. It decreases by 6m.
