The value that makes both sides equal
A solution is a value of the letter-number that makes LHS = RHS.
Which arrangement has 99 sticks?
Jasmine’s equation is 2n + 1 = 99. Position n = 10 has 2 × 10 + 1 = 21 sticks.
Which position n will have exactly 99 sticks?
What this lesson covers
The idea
Solving an equation means finding the value(s) of the letter-numbers for which the equality holds, that is, for which the LHS becomes equal to the RHS; such a value is a solution.
Which arrangement has 99 sticks?
Jasmine’s equation is 2n + 1 = 99. Position *n* = 10 has 2 × 10 + 1 = 21 sticks.
Which position *n* will have exactly 99 sticks?
- About 10
- About 50
- About 99
Put a value in both sides
Tap a value. It goes into the LHS and the RHS. The scale shows whether the two sides come out equal.
The solution is the value, not the sides
Only one value of *n* made 2n + 1 equal to 99. Every other value left the sides different.
So *n* = 49 is the solution. The solution is the value of the letter-number (49), not the value of the sides (99).
Solving an equation means finding the value of the letter-number for which the equality holds, that is, for which the LHS becomes equal to the RHS. Such a value is a solution.
- *n* | LHS 2n + 1 | RHS | Equal?
- 10 | 21 | 99 | no
- 30 | 61 | 99 | no
- 40 | 81 | 99 | no
- 50 | 101 | 99 | no
- 49 | 99 | 99 | yes
Notes
A solution of an equation is a value of the letter-number that makes the LHS equal to the RHS. Solving means finding it: here *n* = 49.
Check yourself
Which value is a solution of m + 6 = 15?
Find the solution of 4y = 28: the value of *y* that makes both sides equal.
Answer: 7
4 × 7 = 28, so y = 7 makes LHS = RHS.
Maya puts *n* = 5 in 2n + 1 = 99. The LHS comes out as 11. She says “the solution is 11”. What is wrong?
Find the value of *z* that makes z + 7 = 2 true.
Answer: -5
−5 + 7 = 2, so z = −5.
- 9 — correct. Yes! 9 + 6 = 15, so both sides are equal.
- 6. With m = 6 the LHS is 6 + 6 = 12, not 15.
- 21. With m = 21 the LHS is 21 + 6 = 27, not 15.
- Nothing: 11 is the solution.. If *n* = 11, the LHS is 2 × 11 + 1 = 23, not 99. So 11 is not the solution.
- She should have got 99 for the LHS when she put in 5.. The LHS only becomes 99 for the right *n*. For *n* = 5 it is 11, and that tells us 5 is not a solution.
- 11 is the value of the LHS. A solution is a value of *n* that makes the LHS equal to 99. — correct. Yes! The solution is a value of the letter-number, not the value of a side.