Substitute the given values into the expression to create the table. Analyze the pattern carefully to get the conclusions.
Evaluation: See solution. Pattern: Each value of x is doubled and then increased by 2. Solution: 13
Practice makes perfect
We are given the expression, and we want to evaluate it for different values of x and analyze the emerging pattern.
2x + 2
Let's start by substituting the first value x=- 2 into the expression and simplifying following the order of operations.
For the value x=- 2 our expression simplifies to - 2. We can do the same for other values as well. For this we will use a table to organize our information.
x
2x+2
Result
-2
2( -2) +2
- 2
-1
2( -1) +2
0
0
2( 0) +2
2
1
2( 1) +2
4
2
2( 2) +2
6
3
2( 3) +2
8
Notice that for each result, the value increases by 2. We will use this conclusion to solve the equation 2x+2=28. Since x=-1 gives us a result of 0, we can calculate how many times we would need to increase x before the result gives 28.
28÷ 2= 14 times
We would need to increase x 14 times. This means that the value for x that will solve the equation is -1+ 14=13. Let's check our theory by substituting 13 into the given equation and simplifying.
