Answer :
Let's examine the expressions to determine which ones are equivalent to the expression [tex]\(-6.3x - 4.2\)[/tex].
1. Expression: [tex]\(-53x - 42 - x\)[/tex]
Simplify this expression:
[tex]\[
-53x - x - 42 = -54x - 42
\][/tex]
Clearly, [tex]\(-54x - 42\)[/tex] is not the same as [tex]\(-6.3x - 4.2\)[/tex].
2. Expression: [tex]\(-34 - 53x - 8\)[/tex]
Simplify this expression:
[tex]\[
-34 - 8 - 53x = -42 - 53x
\][/tex]
So, [tex]\(-42 - 53x\)[/tex] is not equal to [tex]\(-6.3x - 4.2\)[/tex].
3. Expression: [tex]\(47 - 23x + 5 - 4x\)[/tex]
Simplify this expression:
[tex]\[
47 + 5 - 23x - 4x = 52 - 27x
\][/tex]
Therefore, [tex]\(52 - 27x\)[/tex] is different from [tex]\(-6.3x - 4.2\)[/tex].
4. Expression: [tex]\(-52x - 42\)[/tex]
As it stands, this expression is clearly different from [tex]\(-6.3x - 4.2\)[/tex].
5. Expression: [tex]\(-42x - 6.3\)[/tex]
Simplified already, this expression is not equivalent to [tex]\(-6.3x - 4.2\)[/tex].
6. Expression: [tex]\(-37 - 53x + 0.5\)[/tex]
Simplify this expression:
[tex]\[
-37 + 0.5 - 53x = -36.5 - 53x
\][/tex]
As such, [tex]\(-36.5 - 53x\)[/tex] is not equivalent to [tex]\(-6.3x - 4.2\)[/tex].
In conclusion, none of the given expressions are equivalent to [tex]\(-6.3x - 4.2\)[/tex]. Each simplification process returns a result that differs from the target expression.
1. Expression: [tex]\(-53x - 42 - x\)[/tex]
Simplify this expression:
[tex]\[
-53x - x - 42 = -54x - 42
\][/tex]
Clearly, [tex]\(-54x - 42\)[/tex] is not the same as [tex]\(-6.3x - 4.2\)[/tex].
2. Expression: [tex]\(-34 - 53x - 8\)[/tex]
Simplify this expression:
[tex]\[
-34 - 8 - 53x = -42 - 53x
\][/tex]
So, [tex]\(-42 - 53x\)[/tex] is not equal to [tex]\(-6.3x - 4.2\)[/tex].
3. Expression: [tex]\(47 - 23x + 5 - 4x\)[/tex]
Simplify this expression:
[tex]\[
47 + 5 - 23x - 4x = 52 - 27x
\][/tex]
Therefore, [tex]\(52 - 27x\)[/tex] is different from [tex]\(-6.3x - 4.2\)[/tex].
4. Expression: [tex]\(-52x - 42\)[/tex]
As it stands, this expression is clearly different from [tex]\(-6.3x - 4.2\)[/tex].
5. Expression: [tex]\(-42x - 6.3\)[/tex]
Simplified already, this expression is not equivalent to [tex]\(-6.3x - 4.2\)[/tex].
6. Expression: [tex]\(-37 - 53x + 0.5\)[/tex]
Simplify this expression:
[tex]\[
-37 + 0.5 - 53x = -36.5 - 53x
\][/tex]
As such, [tex]\(-36.5 - 53x\)[/tex] is not equivalent to [tex]\(-6.3x - 4.2\)[/tex].
In conclusion, none of the given expressions are equivalent to [tex]\(-6.3x - 4.2\)[/tex]. Each simplification process returns a result that differs from the target expression.
