For each equation, choose the statement that describes its solution. if applicable, give the solution.

5(y+1)-7 = 3(y-1)+2y

no solution

y = ?

all real numbers are solutions

This equation has no solution.

Step-by-step explanation:

Perform the indicated multiplication:  5(y+1)-7 = 3(y-1)+2y

We get 5y + 5 - 7 = 3y - 3 + 2y.  Subtracting 5y from both sides yields -2 = -3, which is never true.  This equation has no solution.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)