Answer :
Sure! Let's go through the problem step-by-step:
Problem: The difference between [tex]\( x \)[/tex] and 89 is 7.
To solve this, we can write this relationship as an equation. There are several ways to express this difference mathematically, but only one will correctly describe the problem and lead us to the right solution.
### Let's examine each option:
Option 1:
- Equation: [tex]\( 89 - x = 7 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
89 - x = 7
\][/tex]
Subtract 7 from both sides:
[tex]\[
89 - 7 = x
\][/tex]
So,
[tex]\[
x = 82
\][/tex]
This satisfies the condition [tex]\( 89 - 82 = 7 \)[/tex].
Option 2:
- Equation: [tex]\( x - 89 = 7 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
x - 89 = 7
\][/tex]
Add 89 to both sides:
[tex]\[
x = 7 + 89
\][/tex]
So,
[tex]\[
x = 96
\][/tex]
This satisfies the condition [tex]\( 96 - 89 = 7 \)[/tex].
Option 3:
- Equation: [tex]\( x - 7 = 89 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
x - 7 = 89
\][/tex]
Add 7 to both sides:
[tex]\[
x = 89 + 7
\][/tex]
So,
[tex]\[
x = 96
\][/tex]
This satisfies the condition [tex]\( 96 - 89 = 7 \)[/tex].
Option 4:
- Equation: [tex]\( 7 - x = 89 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
7 - x = 89
\][/tex]
Subtract 7 from both sides:
[tex]\[
-x = 89 - 7
\][/tex]
So,
[tex]\[
-x = 82 \implies x = -82
\][/tex]
This does not satisfy the given condition as [tex]\( 7 - (-82) = 89 \)[/tex] does not match.
### Conclusion:
- Option 1: Equation [tex]\( 89 - x = 7 \)[/tex] gives [tex]\( x = 82 \)[/tex]. This is a correct solution.
- Option 2: Equation [tex]\( x - 89 = 7 \)[/tex] gives [tex]\( x = 96 \)[/tex]. This is a correct solution.
- Option 3: Equation [tex]\( x - 7 = 89 \)[/tex] gives [tex]\( x = 96 \)[/tex]. This is a correct solution.
- Option 4: Equation [tex]\( 7 - x = 89 \)[/tex] gives [tex]\( x = -82 \)[/tex]. This does not match the problem description.
Thus, the equations that model the problem correctly are:
1. [tex]\( 89 - x = 7 \)[/tex] leading to the answer [tex]\( x = 82 \)[/tex].
2. [tex]\( x - 89 = 7 \)[/tex] leading to the answer [tex]\( x = 96 \)[/tex].
3. [tex]\( x - 7 = 89 \)[/tex] leading to the answer [tex]\( x = 96 \)[/tex].
So, the properly modeled equations and their respective solutions are:
1. [tex]\( 89 - x = 7 \)[/tex], giving [tex]\( x = 82 \)[/tex].
2. [tex]\( x - 89 = 7 \)[/tex], giving [tex]\( x = 96 \)[/tex].
3. [tex]\( x - 7 = 89 \)[/tex], giving [tex]\( x = 96 \)[/tex].
The correct responses based on the given options are:
- Write the equation as [tex]\( x - 89 = 7 \)[/tex] and add 89 to both sides. The answer is 96.
- Write the equation as [tex]\( x - 7 = 89 \)[/tex] and add 7 to both sides. The answer is 96.
Problem: The difference between [tex]\( x \)[/tex] and 89 is 7.
To solve this, we can write this relationship as an equation. There are several ways to express this difference mathematically, but only one will correctly describe the problem and lead us to the right solution.
### Let's examine each option:
Option 1:
- Equation: [tex]\( 89 - x = 7 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
89 - x = 7
\][/tex]
Subtract 7 from both sides:
[tex]\[
89 - 7 = x
\][/tex]
So,
[tex]\[
x = 82
\][/tex]
This satisfies the condition [tex]\( 89 - 82 = 7 \)[/tex].
Option 2:
- Equation: [tex]\( x - 89 = 7 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
x - 89 = 7
\][/tex]
Add 89 to both sides:
[tex]\[
x = 7 + 89
\][/tex]
So,
[tex]\[
x = 96
\][/tex]
This satisfies the condition [tex]\( 96 - 89 = 7 \)[/tex].
Option 3:
- Equation: [tex]\( x - 7 = 89 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
x - 7 = 89
\][/tex]
Add 7 to both sides:
[tex]\[
x = 89 + 7
\][/tex]
So,
[tex]\[
x = 96
\][/tex]
This satisfies the condition [tex]\( 96 - 89 = 7 \)[/tex].
Option 4:
- Equation: [tex]\( 7 - x = 89 \)[/tex]
- To solve for [tex]\( x \)[/tex]:
[tex]\[
7 - x = 89
\][/tex]
Subtract 7 from both sides:
[tex]\[
-x = 89 - 7
\][/tex]
So,
[tex]\[
-x = 82 \implies x = -82
\][/tex]
This does not satisfy the given condition as [tex]\( 7 - (-82) = 89 \)[/tex] does not match.
### Conclusion:
- Option 1: Equation [tex]\( 89 - x = 7 \)[/tex] gives [tex]\( x = 82 \)[/tex]. This is a correct solution.
- Option 2: Equation [tex]\( x - 89 = 7 \)[/tex] gives [tex]\( x = 96 \)[/tex]. This is a correct solution.
- Option 3: Equation [tex]\( x - 7 = 89 \)[/tex] gives [tex]\( x = 96 \)[/tex]. This is a correct solution.
- Option 4: Equation [tex]\( 7 - x = 89 \)[/tex] gives [tex]\( x = -82 \)[/tex]. This does not match the problem description.
Thus, the equations that model the problem correctly are:
1. [tex]\( 89 - x = 7 \)[/tex] leading to the answer [tex]\( x = 82 \)[/tex].
2. [tex]\( x - 89 = 7 \)[/tex] leading to the answer [tex]\( x = 96 \)[/tex].
3. [tex]\( x - 7 = 89 \)[/tex] leading to the answer [tex]\( x = 96 \)[/tex].
So, the properly modeled equations and their respective solutions are:
1. [tex]\( 89 - x = 7 \)[/tex], giving [tex]\( x = 82 \)[/tex].
2. [tex]\( x - 89 = 7 \)[/tex], giving [tex]\( x = 96 \)[/tex].
3. [tex]\( x - 7 = 89 \)[/tex], giving [tex]\( x = 96 \)[/tex].
The correct responses based on the given options are:
- Write the equation as [tex]\( x - 89 = 7 \)[/tex] and add 89 to both sides. The answer is 96.
- Write the equation as [tex]\( x - 7 = 89 \)[/tex] and add 7 to both sides. The answer is 96.
