Answer :
Sure! Let's solve the problem step-by-step.
We need to create and solve a linear equation that represents the given model. The options given are:
1. [tex]\( x = 5 + 7 ; x = 12 \)[/tex]
2. [tex]\( x + 7 = 5 ; x = -2 \)[/tex]
3. [tex]\( x + 5 = 7 ; x = 2 \)[/tex]
4. [tex]\( x + 7 = 12 ; x = 5 \)[/tex]
Now let's solve each equation to see which one is valid.
### Option 1: [tex]\( x = 5 + 7 ; x = 12 \)[/tex]
The equation here says:
[tex]\[ x = 5 + 7 \][/tex]
Simplifying the right-hand side, we get:
[tex]\[ x = 12 \][/tex]
So, this is correct. However, this was given directly and does not represent an equation solved for [tex]\( x \)[/tex].
### Option 2: [tex]\( x + 7 = 5 ; x = -2 \)[/tex]
The equation here says:
[tex]\[ x + 7 = 5 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 7 from both sides:
[tex]\[ x + 7 - 7 = 5 - 7 \][/tex]
[tex]\[ x = -2 \][/tex]
This is correct as well.
### Option 3: [tex]\( x + 5 = 7 ; x = 2 \)[/tex]
The equation here says:
[tex]\[ x + 5 = 7 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 5 from both sides:
[tex]\[ x + 5 - 5 = 7 - 5 \][/tex]
[tex]\[ x = 2 \][/tex]
This is also correct.
### Option 4: [tex]\( x + 7 = 12 ; x = 5 \)[/tex]
The equation here says:
[tex]\[ x + 7 = 12 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 7 from both sides:
[tex]\[ x + 7 - 7 = 12 - 7 \][/tex]
[tex]\[ x = 5 \][/tex]
This is also correct.
Among the options, the one that represents both a valid equation and shows [tex]\( x \)[/tex] solved, where [tex]\( x + 7 = 12 ; x = 5 \)[/tex], is the most suitable as it correctly models and provides the solution.
Thus, the correct answer is:
[tex]\[ x + 7 = 12 ; x = 5 \][/tex]
Therefore, the correct option is:
### [tex]\( x + 7 = 12 ; x = 5 \)[/tex]
We need to create and solve a linear equation that represents the given model. The options given are:
1. [tex]\( x = 5 + 7 ; x = 12 \)[/tex]
2. [tex]\( x + 7 = 5 ; x = -2 \)[/tex]
3. [tex]\( x + 5 = 7 ; x = 2 \)[/tex]
4. [tex]\( x + 7 = 12 ; x = 5 \)[/tex]
Now let's solve each equation to see which one is valid.
### Option 1: [tex]\( x = 5 + 7 ; x = 12 \)[/tex]
The equation here says:
[tex]\[ x = 5 + 7 \][/tex]
Simplifying the right-hand side, we get:
[tex]\[ x = 12 \][/tex]
So, this is correct. However, this was given directly and does not represent an equation solved for [tex]\( x \)[/tex].
### Option 2: [tex]\( x + 7 = 5 ; x = -2 \)[/tex]
The equation here says:
[tex]\[ x + 7 = 5 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 7 from both sides:
[tex]\[ x + 7 - 7 = 5 - 7 \][/tex]
[tex]\[ x = -2 \][/tex]
This is correct as well.
### Option 3: [tex]\( x + 5 = 7 ; x = 2 \)[/tex]
The equation here says:
[tex]\[ x + 5 = 7 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 5 from both sides:
[tex]\[ x + 5 - 5 = 7 - 5 \][/tex]
[tex]\[ x = 2 \][/tex]
This is also correct.
### Option 4: [tex]\( x + 7 = 12 ; x = 5 \)[/tex]
The equation here says:
[tex]\[ x + 7 = 12 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 7 from both sides:
[tex]\[ x + 7 - 7 = 12 - 7 \][/tex]
[tex]\[ x = 5 \][/tex]
This is also correct.
Among the options, the one that represents both a valid equation and shows [tex]\( x \)[/tex] solved, where [tex]\( x + 7 = 12 ; x = 5 \)[/tex], is the most suitable as it correctly models and provides the solution.
Thus, the correct answer is:
[tex]\[ x + 7 = 12 ; x = 5 \][/tex]
Therefore, the correct option is:
### [tex]\( x + 7 = 12 ; x = 5 \)[/tex]
