Question

check for understanding
which statement below is true?
a) $8 + 2 + n = 1 + 10 + n$
b) $2x + 3 < x + x + x + 3$
c) $7 + n + 3 = 2 + 8 + n$
d) $n + n + n + 4 = 2n + 2 + 2$

Explanation:

Step1: Simplify option a

Left side: $8+2+n=10+n$
Right side: $1+10+n=11+n$
$10+n
eq 11+n$, so a is false.

Step2: Simplify option b

Left side: $2x+3$
Right side: $x+x+x+3=3x+3$
$2x+3 < 3x+3$ simplifies to $0 < x$, which is only true for $x>0$, not all $x$. So b is false.

Step3: Simplify option c

Left side: $7+n+3=10+n$
Right side: $2+8+n=10+n$
$10+n = 10+n$, so c is true.

Step4: Verify option d (optional)

Left side: $n+n+n+4=3n+4$
Right side: $2n+2+2=2n+4$
$3n+4
eq 2n+4$ (unless $n=0$), so d is false.

Answer:

c) $7 + n + 3 = 2 + 8 + n$