Question

does the equation 2(4x + 5) = 10x + 2 have one solution, no solutions, or infinitely many solutions? we can distribute the 2 to rewrite the left side of the equation without parentheses. you can think of this as (2 · 4x) + (2 · 5). rewrite the left side. 2(4x + 5) =
□ + □ = 10x + 2

Explanation:

Step1: Distribute the 2 to terms inside

$2(4x + 5) = (2 \cdot 4x) + (2 \cdot 5) = 8x + 10$

Step2: Set equal to right side, simplify

$8x + 10 = 10x + 2$
Subtract $8x$ from both sides: $10 = 2x + 2$
Subtract 2 from both sides: $8 = 2x$
Divide by 2: $x = 4$

Answer:

The rewritten left side is $\boldsymbol{8x + 10}$. The equation has one solution, which is $\boldsymbol{x=4}$.