a How can you tell if a value is a solution to an equation?
B
b For which values of x are both sides of the equation getting closer to each other?
C
c Check the spreadsheet values.
A
a No.
B
b The solution must be between -3 and -1. See solution.
C
c x=-5 and x= -3
Practice makes perfect
a The exercise tell us to work out the equation 7(x+1) = 3(x-1) using the spreadsheet shown below. We are asked if the solution of the equation is shown in the spreadsheet.
A
B
C
1
x
7(x+1)
3(x-1)
2
-5
-28
-18
3
-3
-14
-12
4
-1
0
-6
5
1
14
0
6
3
28
6
A value is a solution for an equation if substituting it into the equation makes a true statement. In this case, we are evaluating the expressions 7(x+1) and 3(x-1) for certain values of x. If one of them was the solution for the equation 7(x+1) = 3(x-1), then both expressions would produce the same number for that specific x-value. We can see that this does not happen. Therefore, the solution isn't shown.
b This time, we are asked between which x-values the solution is and how we know. Notice that the solution would be the x-value that makes
7(x+1) equal to 3(x-1). Let's start by analyzing the given values and the difference between 7(x+1) and 3(x-1).
A
B
C
D
1
x
7(x+1)
3(x-1)
| 7(x+1) - 3(x-1)|
2
-5
-28
-18
10
3
-3
-14
-12
2
4
-1
0
-6
6
5
1
14
0
14
6
3
28
6
22
As we can see, the value of 7(x+1) was getting closer to the value of 3(x-1) until x reached the value -1. After that, their values started to get further away from one another. This means that the solution must be between -3 and -1.
c Now, we want to know for which values of x is 7(x+1) less than 3(x-1). Let's look at the spreadsheet values to see which x values fulfill this requirement.
A
B
C
D
1
x
7(x+1)
3(x-1)
7(x+1) < 3(x-1)
2
-5
-28
-18
✓
3
-3
-14
-12
✓
4
-1
0
-6
*
5
1
14
0
*
6
3
28
6
*
We can see that this is only true for the values x=-5 and x= -3.
