Answer :
We need to translate the statement "3 more than 8 times a number [tex]\(x\)[/tex] is equal to 83" into an equation.
1. "8 times a number [tex]\(x\)[/tex]" translates to:
[tex]$$8x$$[/tex]
2. "3 more than 8 times a number [tex]\(x\)[/tex]" means we add 3 to [tex]\(8x\)[/tex], giving:
[tex]$$8x + 3$$[/tex]
3. Since the statement says this expression is equal to 83, we have:
[tex]$$8x + 3 = 83$$[/tex]
To verify the equation, we can solve for [tex]\(x\)[/tex]:
- Subtract 3 from both sides:
[tex]$$8x = 83 - 3 = 80$$[/tex]
- Divide both sides by 8:
[tex]$$x = \frac{80}{8} = 10$$[/tex]
When [tex]\(x=10\)[/tex] is substituted back:
[tex]$$8(10) + 3 = 80 + 3 = 83$$[/tex]
This confirms that the equation is correct.
Thus, the equation that represents the situation is:
[tex]$$8x + 3 = 83$$[/tex]
This corresponds to choice 4.
1. "8 times a number [tex]\(x\)[/tex]" translates to:
[tex]$$8x$$[/tex]
2. "3 more than 8 times a number [tex]\(x\)[/tex]" means we add 3 to [tex]\(8x\)[/tex], giving:
[tex]$$8x + 3$$[/tex]
3. Since the statement says this expression is equal to 83, we have:
[tex]$$8x + 3 = 83$$[/tex]
To verify the equation, we can solve for [tex]\(x\)[/tex]:
- Subtract 3 from both sides:
[tex]$$8x = 83 - 3 = 80$$[/tex]
- Divide both sides by 8:
[tex]$$x = \frac{80}{8} = 10$$[/tex]
When [tex]\(x=10\)[/tex] is substituted back:
[tex]$$8(10) + 3 = 80 + 3 = 83$$[/tex]
This confirms that the equation is correct.
Thus, the equation that represents the situation is:
[tex]$$8x + 3 = 83$$[/tex]
This corresponds to choice 4.
