Question

select all of the equations below that are equivalent to:
19 = b + 20
use properties of equality.
9 = b + 20 − 9
17 = b + 20 − 2
19 − 6 = b + 13
3 = b + 20 − 17

Explanation:

Step1: Find $b$ from original equation

$19 = b + 20 \implies b = 19 - 20 = -1$

Step2: Test first equation: $9 = b + 20 - 9$

Simplify right-hand side: $b + 11$. Substitute $b=-1$: $-1 + 11 = 10
eq 9$

Step3: Test second equation: $17 = b + 20 - 2$

Simplify right-hand side: $b + 18$. Substitute $b=-1$: $-1 + 18 = 17 = 17$

Step4: Test third equation: $19 - 6 = b + 13$

Simplify left-hand side: $13$. Substitute $b=-1$: $-1 + 13 = 12
eq 13$

Step5: Test fourth equation: $3 = b + 20 - 17$

Simplify right-hand side: $b + 3$. Substitute $b=-1$: $-1 + 3 = 2
eq 3$

Answer:

$17 = b + 20 - 2$