9514 1404 393
Answer:
- x=2 (work is correct)
- x=4
- x=44
- x=4
- x=any number
- impossible; no such number
Step-by-step explanation:
1. The equation is ...
3x +5 = 11
3x = 11 -5 = 6
x = 6/3 = 2 . . . . matches the work shown
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2. The equation is ...
(x +2)·5 = 30
x +2 = 30/5 = 6
x = 6 -2 = 4
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3. The equation is ...
(x/2) +2 = 24 . . . . matches the work shown
x/2 = 24 -2 = 22
x = 22·2 = 44
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4. The equation is ...
2x +8 = x +12
2x = x + 12 -8 = x +4
2x -x = x -x +4
x = 4
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5. The equation is ...
2x +4 -x -3 = x +1
x +1 = x +1 . . . . . true for any value of x
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6. The equation is ...
(3x +6) -2x = x +3
x +6 = x +3 . . . . . not true for any number
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Additional comment
The work shown is correct. You find x by writing and solving an appropriate equation. To solve the equation, undo the steps that are done to x. Undo addition by adding the opposite. Undo multiplication by diving by the multiplier. It often helps to collect terms before you start the "undo" steps.
For x on both sides of the equation (as in problems 4–6), you can subtract the term with the lowest coefficient. (Of course, you must subtract it from both sides of the equation.) In problem 5, if you do that, you get 1=1, which is true for any value of x. In problem 6, if you do that, you get 6=3, a false equation, indicating no value of x will make it true.
