Answer :
To solve the problem, we need to model the statement "The difference between [tex]\( x \)[/tex] and 89 is 7" with an equation. Here are the steps to find the correct equation and solution:
1. Understanding the Statement:
- The phrase "the difference between [tex]\( x \)[/tex] and 89 is 7" means that when you subtract 89 from [tex]\( x \)[/tex], the result is 7. This can be written as:
[tex]\[
x - 89 = 7
\][/tex]
2. Solving the Equation:
- To solve the equation [tex]\( x - 89 = 7 \)[/tex], we need to add 89 to both sides of the equation to isolate [tex]\( x \)[/tex]:
[tex]\[
x - 89 + 89 = 7 + 89
\][/tex]
- Simplifying both sides gives:
[tex]\[
x = 96
\][/tex]
3. Checking Other Options:
- Option 1: [tex]\( 89 - x = 7 \)[/tex]: This setup implies subtracting [tex]\( x \)[/tex] from 89. Solving yields [tex]\( x = 82 \)[/tex], which doesn't match the intended meaning of the original statement.
- Option 3: [tex]\( x - 7 = 89 \)[/tex]: Solving for [tex]\( x \)[/tex], we get [tex]\( x = 89 + 7 = 96 \)[/tex]. This equation also leads to the correct result if rewritten appropriately.
- Option 4: [tex]\( 7 - x = 89 \)[/tex]: This doesn't match the independent statement at all.
Given our examination, the equation [tex]\( x - 89 = 7 \)[/tex] and its solution [tex]\( x = 96 \)[/tex] fits the problem description perfectly. Thus, the correct solution is to write the equation as [tex]\( x - 89 = 7 \)[/tex] and add 89 to both sides, resulting in [tex]\( x = 96 \)[/tex].
1. Understanding the Statement:
- The phrase "the difference between [tex]\( x \)[/tex] and 89 is 7" means that when you subtract 89 from [tex]\( x \)[/tex], the result is 7. This can be written as:
[tex]\[
x - 89 = 7
\][/tex]
2. Solving the Equation:
- To solve the equation [tex]\( x - 89 = 7 \)[/tex], we need to add 89 to both sides of the equation to isolate [tex]\( x \)[/tex]:
[tex]\[
x - 89 + 89 = 7 + 89
\][/tex]
- Simplifying both sides gives:
[tex]\[
x = 96
\][/tex]
3. Checking Other Options:
- Option 1: [tex]\( 89 - x = 7 \)[/tex]: This setup implies subtracting [tex]\( x \)[/tex] from 89. Solving yields [tex]\( x = 82 \)[/tex], which doesn't match the intended meaning of the original statement.
- Option 3: [tex]\( x - 7 = 89 \)[/tex]: Solving for [tex]\( x \)[/tex], we get [tex]\( x = 89 + 7 = 96 \)[/tex]. This equation also leads to the correct result if rewritten appropriately.
- Option 4: [tex]\( 7 - x = 89 \)[/tex]: This doesn't match the independent statement at all.
Given our examination, the equation [tex]\( x - 89 = 7 \)[/tex] and its solution [tex]\( x = 96 \)[/tex] fits the problem description perfectly. Thus, the correct solution is to write the equation as [tex]\( x - 89 = 7 \)[/tex] and add 89 to both sides, resulting in [tex]\( x = 96 \)[/tex].
