Simple Algebra Problem: Finding the Product of Consecutive Even Integers

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So, x=6 or -8.In summary, the problem is to find two consecutive even integers that have a product of 48. The correct equation to solve is x^2 + 2x = 48, but dividing by 2x will not give the correct solution. The equation should be rewritten as x^2 + 2x - 48 = 0 and solved using the quadratic equation. The solutions are x = 6 or x = -8, but since the problem states "consecutive even integers," the correct solution is x = 6. Another way to solve the problem is by factoring the equation to (x-6)(x+8) = 0, which also gives the solution
  • #1
kuahji
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Ok, I have a simple algebra problem I need help with.

The problem states "The product of two consecutive even integers is 48."
So I wrote the equation out as x(x+2)=48. If I factor that I should get x^2+2x=48? Then divide 48 by 2x & get 24. Then squard root of 24? What step am I doing incorrect? I've been racking my brain on this problem for like a half an hour :-p (this is what I get for being out of school for 4 years). I mean the answer is simple 6 x 8 = 48. But, I would like to know the steps. Any help is appreciated.
 
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  • #2
kuahji said:
Ok, I have a simple algebra problem I need help with.

The problem states "The product of two consecutive even integers is 48."
So I wrote the equation out as x(x+2)=48. If I factor that I should get x^2+2x=48? Then divide 48 by 2x & get 24. Then squard root of 24? What step am I doing incorrect? I've been racking my brain on this problem for like a half an hour :-p (this is what I get for being out of school for 4 years). I mean the answer is simple 6 x 8 = 48. But, I would like to know the steps. Any help is appreciated.

ok so you have
[tex] x(x+2) = 48 [/tex]
[tex] x^2 +2x = 48[/tex]

The thing is that you can't just divide by 2x and get [tex] x^2 = 24[/tex]
rewrite the equation as
[tex] x^2 + 2x - 48 = 0[/tex]

then use the quadratic equation to solve for x, and take the solution that fits the problem's description.
 
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  • #3
d_leet said:
ok so you have
[tex] x(x+2) = 48
x^2 +2x = 48[/tex]
The thing is that you can't just divide by 2x and get [tex] x^2 = 24[/tex]
rewrite the equation as
[tex] x^2 + 2x - 48 = 0[/tex]
then use the quadratic equation to solve for x, and take the solution that fits the problem's description.

Ok, brilliant. Thanks much for your help. It is greatly appreciated :cool:. The algebra rules are slowly coming back to me.
 
  • #4
Yeah, if you divide [tex]x^2 + 2x = 48[/tex] by 2x then you get:

[tex]\frac {1}{2}x + 1 = \frac {24}{x}[/tex]

Doesn't really get you anywhere. You have to factor to:
[tex](x-6)(x+8) = 0[/tex]
 
  • #5
One more way. x^2+2x=(x+1)^2-1. So, (x+1)^2=49 So, x+1=(+/-)7
 

FAQ: Simple Algebra Problem: Finding the Product of Consecutive Even Integers

What is an algebraic expression?

An algebraic expression is a mathematical statement that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a generalization of arithmetic and allows for the use of symbols to represent unknown values.

What is the difference between an equation and an expression?

An equation is a statement that shows that two quantities are equal, while an expression is a mathematical statement that may or may not have an equal sign. In other words, an equation is a statement of equality, while an expression is a mathematical phrase.

How do you solve a simple algebraic equation?

To solve a simple algebraic equation, you need to isolate the variable on one side of the equal sign by using inverse operations. This means that you perform the opposite operation to both sides of the equation until the variable is alone on one side. Remember to apply the same operation to both sides of the equation to maintain balance.

What is the order of operations in algebra?

The order of operations in algebra is the same as in arithmetic. The acronym PEMDAS can help you remember the correct order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is important to follow this order to get the correct answer when solving algebraic problems.

How can I check if my solution to an algebraic problem is correct?

To check if your solution to an algebraic problem is correct, you can substitute the value you found for the variable back into the original equation and see if it makes the equation true. You can also use a calculator to evaluate the expression and compare it to your solution. Another option is to graph the equation and see if the point you found for the variable lies on the graph.

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