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seven times a number and 7 is equal to six times a number

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Seven times a number and seven is equal to six times a number.
  • Word problems can be tricky no matter what level of math or science you are in.
  • First look at the question for words that indicate mathematical symbols.
  • "times" indicates multiplication
  • "and" indicates addition
  • "a number" means we have a variable, x, to solve for
  • Now we can go from left to right and write it in a mathematical equation
7x + 7 = 6x
  • Then, solve for x
7x + 7 = 6x
7 = 6x - 7x
7 = -1x
7/-1 = x
x = -7
  • Finally, we check our work.
7x + 7 = 6x
7(-7) + 7 = 6(-7)
-49 + 7 = -42
-42 = -42
 
The answer is x = -7
Seven times a number and seven is equal to six times a number.
 
Step 1:  Translate the verbal to Algebra.
 
7x + 7 = 6x.  ("And" means addition if no other operation is present.)
 
Step 2:  Solve for x.
 
7x - 6x + 7 = 6x - 6x.      (subtract 6x from both sides)
 
1x + 7 = 0.             (Simplify)
 
1x + 7 - 7 = 0 - 7.      (subtract 7 from both sides)
 
1x = -7.             (Simplify)
 
1x/1 = -7/1.        (Divide both sides by 1)
 
x = -7.              (Simplify)
 
Step 3:  Check 7 times the number -7 and 7 is equal to six times the number -7.
 
7(-7) + 7 = 6(-7)
 
-49 + 7 = -42
 
-42 = -42.   (Both sides are equal!)
 
The number again is -7.
 
 First thing you do in word problems : choose a variable for unknown, what problem is asked you to find.
 
       n    the number
     
       7n     7 times the number
 
        7n + 7       7 times the number and 7
 
      Then the problem says it is equal  6n , make the equation
 
       7n + 7 = 6n
 
       and solve:
 
        7n - 6n = -7
 
         n = -7  / is the answer
 
      
 
Hi Alyson;
7x+7=6x
Let's subtract 7x from both sides...
7x+7-7x=6x-7x
7=-x
Let's multiply both sides by -1...
(-1)(7)=(-1)(-x)
-7=x
Let's check our work...
7x+7=6x
[(7)(-7)]+7=(6)(-7)
-49+7=-42
-42=-42