Substitute the values y=1, y=2, and y=3 into each expression and simplify. Then, to determine which expressions are equivalent, check which expressions have the same values for y=1, y=2, and y=3.
Table:
y
5(2.2y+1)-3
11y+5-y
11y+2
1
13
15
13
2
24
25
24
3
35
35
35
Equivalent Expressions: 5(2.2y+1)-3 and 11y+2
Practice makes perfect
We are asked to complete the following table.
y
5(2.2y+1)-3
11y+5-y
11y+2
1
2
3
To complete the table, we need to evaluate three expressions for y=1, y=2, and y=3. Let's do it! We can start with 5(2.2y+1)-3.
5(2.2y+1)-3
We will substitute y=1, y=2, and y=3 into 5(2.2y+1)-3 and then evaluate the expressions following the order of operations.
y
Substitute into 5(2.2y+1)-3
Multiply Terms
Add terms
Multiply Terms
Subtract Terms
1
5(2.2( 1 )+1)-3
5(2.2+1)-3
5(3.2)-3
16-3
13
2
5(2.2( 2 )+1)-3
5(4.4+1)-3
5(5.4)-3
27-3
24
3
5(2.2( 3 )+1)-3
5(6.6+1)-3
5(7.6)-3
38-3
35
We evaluated the expression 5(2.2y+1)-3 for y=1, y=2, and y=3. Now we can fill in the first column of the given table.
y
5(2.2y+1)-3
11y+5-y
11y+2
1
13
2
24
3
35
11y+5-y
We can do the same thing for the expression 11y+5-y. Let's substitute!
y
Substitute into 11y+5-y
Multiply Terms
Add and Subtract Terms
1
11( 1)+5- 1
11+5-1
15
2
11( 2)+5- 2
22+5-2
25
3
11( 3)+5- 3
33+5-3
35
Now we can fill in the second column of the given table.
y
5(2.2y+1)-3
11y+5-y
11y+2
1
13
15
2
24
25
3
35
35
11y+2
Next we will find the values of the expression 11y+2 when y=1, y=2, and y=3.
y
Substitute into 11y+2
Multiply Terms
Add Terms
1
11( 1)+2
11+2
13
2
11( 2)+2
22+2
24
3
11( 3)+2
33+2
35
Finally, we can fill in the last column of the given table.
y
5(2.2y+1)-3
11y+5-y
11y+2
1
13
15
13
2
24
25
24
3
35
35
35
We completed the table! Now we will find the equivalent expressions. Notice that the first and last expressions have the same values when y=1, y=2, and y=3.
