Question

does the equation 2(4x + 5) = 10x + 2 have one solution, no solutions, or infinitely many solutions?
now that youve rewritten the left side of the equation without parentheses, take a look. how many solutions does this equation have? you may consider either using the structure of the equation or trying to isolate x on paper to help you figure out how many solutions this equation has.
2(4x + 5) = 10x + 2
8x + 10 = 10x + 2
one solution
no solutions
infinitely many solutions

Explanation:

Step1: Expand left-hand side

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

Step2: Set equal to right-hand side

$8x+10=10x+2$

Step3: Isolate x terms

$10-2=10x-8x$

Step4: Simplify and solve for x

$8=2x \implies x=\frac{8}{2}=4$

Answer:

One solution