Question

select the two expressions that are equivalent to the given expression
4(x+3)-10+6x
a. 2(5x+1)
b. 10x-7
c. -2x-7
d. 4x+12-10+6x
e. 4x+3 -10+6x
f. 2(8x+1)

Answer 1

Let's first simplify the given expression:

\[ 4(x + 3) - 10 + 6x \]

1. Distribute \(4\) into the parentheses:
\[ 4x + 12 - 10 + 6x \]

2. Combine like terms:
\[ 4x + 6x + 12 - 10 = 10x + 2 \]

So the simplified expression is \(10x + 2\).

Now, let's evaluate the options:

a. \(2(5x + 1)\)
\[ = 10x + 2 \]
This is equivalent.

b. \(10x - 7\)
This is NOT equivalent.

c. \(-2x - 7\)
This is NOT equivalent.

d. \(4x + 12 - 10 + 6x\)
\[ = 10x + 2 \]
This is equivalent.

e. \(4x + 3 - 10 + 6x\)
\[ = 4x + 6x + 3 - 10 = 10x - 7 \]
This is NOT equivalent.

f. \(2(8x + 1)\)
\[ = 16x + 2 \]
This is NOT equivalent.

The two expressions that are equivalent to the original expression \(4(x+3)-10+6x\) are:
- **a. \(2(5x + 1)\)**
- **d. \(4x + 12 - 10 + 6x\)**