C2.3 Solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions.
Activity 1: Strategies for Solving Equations
What strategies can be used to solve the equation below and find the value of m?
2m + 3 = 12
Strategy 1
Reverse Flowchart
I used a reverse flow chart. The top part of the flow chart shows the sequence of operations applied to the variable to obtain the result. The bottom part of the flow chart shows the sequence of the reverse operations to find the value of the variable.
The value of m is 4.5.
Strategy 2
Balance Model
When I used the balance model, I represented the equation algebraically and then manipulated it maintaining equivalence.
First, I collect the terms with the unknown values and isolate them from the terms with the known values. To isolate the term 2m, I remove 3 from it by subtracting 3. To maintain equivalence, what I do on one side of the equal sign, I also need to do on the other. So, I subract 3 from 12 as well.
\(2m \ + \ 3 \ - \ 3 = 12 \ -\ 3\)
\(2m = 9\)
Because 2m means m + m or 2 times m, so in order to know what 1m is I need to divide by 2 and again what I do to one side of the equal sign I need to do on the other so I am aslo diving 9 by 2.
\(\frac{2}{2}m \ = \frac{9}{2}\)
\(m \ = 4.5 \)
The value of m is 4.5.
Source: translated from En avant, les maths!, 7e année, CM, Algèbre, p. 3.
Activity 2: Solving Equations
Solve the problems below and then check your solutions.
- \(3x + 5 = 7x - 3\)
- \(3.5k - 12 = 0.4k + 5\)
- \(-3.1f + 6.2 = 5.5f + 1.8\)