Question

subtraction equations

1. solve the equation by using tape diagrams. then solve the equation algebraically. use substitution to check your solution.

a. $x - 9 = 15$
b. $17 = a - 8$

Explanation:

Part a: $x - 9 = 15$

Step1: Isolate $x$ by adding 9

$x - 9 + 9 = 15 + 9$

Step2: Simplify to find $x$

$x = 24$

Step3: Check solution via substitution

$24 - 9 = 15$
$15 = 15$ (valid)

Part b: $17 = a - 8$

Step1: Isolate $a$ by adding 8

$17 + 8 = a - 8 + 8$

Step2: Simplify to find $a$

$25 = a$

Step3: Check solution via substitution

$17 = 25 - 8$
$17 = 17$ (valid)

Answer:

a. $x = 24$
b. $a = 25$

Tape Diagram Note (Conceptual):

For $x - 9 = 15$: Draw a tape labeled $x$, split into two parts: one labeled 9 and the other labeled 15. The total length $x$ is $9 + 15 = 24$.
For $17 = a - 8$: Draw a tape labeled $a$, split into two parts: one labeled 8 and the other labeled 17. The total length $a$ is $17 + 8 = 25$.