Make this equation or open sentence true, by guessing:
2'x + 3 = 17
What does this mean? We're looking for a number to put in for x so that when we multiply it by 2, then add 3, we should get 17. Notice that the x is not a times sign, it's a variable, holding the place for a number. The dot (') here means multiply.
Let's try 5 in for x, 2'5 + 3 =? 17 is 2'5 + 3 equal to 17? 2'5 = 10
10 + 3 =? 17 is 10 + 3 equal to 17?
13 =? 17 is 13 equal to 17 ? No. 13 =17 is false.
So 5 doesn't work. Is 5 too big or too small? 5 is too small because we get 13 on the left side of the equation, and that's smaller than 17. What shall we try next? 7. OK.
2'7 + 3 =? 17
14 + 3 =? 17
17 = 17 and this is true.
So 7 is the number that works, it makes a true statement, 7 is the answer to
2'x + 3 = 17 {7}
Now solve these equations, make these open sentences true:
2) 2'x + 3 = 18
3) 3'x + 5 = 11
4) 3'x + 5 = 12
What could you change if you made up an equation like these?
Make up some equations like these for a friend and have a friend make up some for you. You might want to change one thing at a time to see what happens. See if you can find some patterns. Stay with one variable.