Question

4 select all the equations that match the tape diagram.
a. $35 = 8 + x + x + x + x + x + x$
b. $35 = 8 + 6x$
c. $6 + 8x = 35$
d. $6x + 8 = 35$
e. $6x + 8x = 35x$
f. $35 - 8 = 6x$

Explanation:

Step1: Analyze the tape diagram

The tape diagram has a part labeled 8 and six parts labeled \( x \), with the total being 35. So the sum of 8 and six \( x \)s equals 35.

Step2: Evaluate Option A

Option A: \( 35 = 8 + x + x + x + x + x + x \). Since there are six \( x \) terms, this is equivalent to \( 35 = 8 + 6x \), so A is correct.

Step3: Evaluate Option B

Option B: \( 35 = 8 + 6x \). This directly matches the tape diagram (8 plus six \( x \)s equals 35), so B is correct.

Step4: Evaluate Option C

Option C: \( 6 + 8x = 35 \). This does not match the tape diagram (the constant term is 8, not 6, and the number of \( x \) terms is 6, not 8), so C is incorrect.

Step5: Evaluate Option D

Option D: \( 6x + 8 = 35 \). This is the same as \( 8 + 6x = 35 \) (addition is commutative), so D is correct.

Step6: Evaluate Option E

Option E: \( 6x + 8x = 35x \). Simplifying the left side gives \( 14x = 35x \), which is not equivalent to the tape diagram equation, so E is incorrect.

Step7: Evaluate Option F

Option F: \( 35 - 8 = 6x \). Subtracting 8 from both sides of \( 35 = 8 + 6x \) gives \( 35 - 8 = 6x \), so F is correct.

Answer:

A. \( 35 = 8 + x + x + x + x + x + x \)
B. \( 35 = 8 + 6x \)
D. \( 6x + 8 = 35 \)
F. \( 35 - 8 = 6x \)