Solving Basic Equations: Tips & Tricks

In summary: You should have written it as 1/(x + 2) = 7. Without the parentheses, 1/x + 2 means (1/x) + 2, which is not what you intend.[/quote]In summary, the students got the answers for equation b and c wrong. They should have written 1/(x + 2) = 7.
  • #1
3
0

Homework Statement



Solve each of the following equations. This is part of a practice mock test I have for an exam so I have all the answers but they aren't lining up somewhere. I got a) right but b) and c) wrong

Homework Equations



a)4x+6=18
b)5x+7=7x-9
c)1/x+2 = 7 (giving answer rounded to 4 decimal places)

The Attempt at a Solution


The first was easy, the rest though :/
a:
4x+6=18
4x=12
x=3

b:
5x+7 = 7x-9
-2X = -2
X= 4


c:
1/x+2 = 7
x+2 = (7*1)
x=5

the answer they got was -1.8571...

Please help guys this basic stuff is killing me! I can do that advanced stuff no problem (this is for a degree in Engineering) but this basic stuff is a nightmare!
 
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  • #2
cording12 said:

Homework Statement



Solve each of the following equations. This is part of a practice mock test I have for an exam so I have all the answers but they aren't lining up somewhere. I got a) right but b) and c) wrong

Homework Equations



a)4x+6=18
b)5x+7=7x-9
c)1/x+2 = 7 (giving answer rounded to 4 decimal places)
You should write this as 1/(x + 2) = 7. Without the parentheses, 1/x + 2 means (1/x) + 2, which is not what you intend.
cording12 said:

The Attempt at a Solution


The first was easy, the rest though :/
a:
4x+6=18
4x=12
x=3

b:
5x+7 = 7x-9
-2X = -2
X= 4
Divide both sides of the equation -2x = -2 by -2. The solution is not x = 4.
cording12 said:
c:
1/x+2 = 7
x+2 = (7*1)
x=5
Again, write the equation as 1/(x + 2) = 7. Now, if two numbers are equal, their reciprocals are equal, so the next equation is
x + 2 = 1/7
Can you finish this?
cording12 said:
the answer they got was -1.8571...

Please help guys this basic stuff is killing me! I can do that advanced stuff no problem (this is for a degree in Engineering) but this basic stuff is a nightmare!
 
  • #3
cording12 said:
b:
5x+7 = 7x-9
-2X = -2
X= 4
Mark44 said:
Divide both sides of the equation -2x = -2 by -2. The solution is not x = 4.
Not only that, but from
5x+7 = 7x-9,
when you move terms around, you don't get
-2x = -2.
 

What is an equation?

An equation is a mathematical statement that shows the relationship between two or more quantities. It typically contains variables, constants, and mathematical operations.

How do I solve a basic equation?

To solve a basic equation, you need to isolate the variable on one side of the equation and perform the same operation on both sides to maintain balance. This can be done by using inverse operations such as addition/subtraction or multiplication/division.

What are some tips for solving equations?

Some tips for solving equations include organizing the equation by combining like terms, using the distributive property, and checking your work by plugging in your solution back into the original equation.

What are common mistakes to avoid when solving equations?

Some common mistakes to avoid when solving equations include forgetting to distribute negative signs, making calculation errors, and not checking your work. It's also important to pay attention to the order of operations and to keep track of positive and negative signs.

Can equations have more than one solution?

Yes, equations can have more than one solution. These are called simultaneous equations and typically have multiple variables. In order to solve them, you need to find values for all variables that satisfy all equations in the system.

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