Question

solve and verify 7y-2/5y-1= 7y+3/5y+1​

Answer 1

Answer:

Step by Step Solution

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                7*y-2/5*y-1-(3+7*y/4+5*y)=0 

Step by step solution :

STEP1:

y Simplify — 4

Equation at the end of step1:

2 y ((7y-(—•y))-1)-((3+(7•—))+5y) = 0 5 4

STEP2:Rewriting the whole as an Equivalent Fraction

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  4  as the denominator :

3 3 • 4 3 = — = ————— 1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3 • 4 + 7y 7y + 12 —————————— = ——————— 4 4

Equation at the end of step2:

2 (7y+12) ((7y-(—•y))-1)-(———————+5y) = 0 5 4

STEP3:

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  4  as the denominator :

5y 5y • 4 5y = —— = —————— 1 4

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions

(7y+12) + 5y • 4 27y + 12 ———————————————— = ———————— 4 4

Equation at the end of step3:

2 (27y + 12) ((7y - (— • y)) - 1) - —————————— = 0 5 4

STEP4:

2 Simplify — 5

Equation at the end of step4:

2 (27y + 12) ((7y - (— • y)) - 1) - —————————— = 0 5 4

STEP5:

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

7y 7y • 5 7y = —— = —————— 1 5

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

7y • 5 - (2y) 33y ————————————— = ——— 5 5

Equation at the end of step5:

33y (27y + 12) (——— - 1) - —————————— = 0 5 4

STEP6:

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

1 1 • 5 1 = — = ————— 1 5

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

33y - (5) 33y - 5 ————————— = ——————— 5 5

Equation at the end of step6:

(33y - 5) (27y + 12) ————————— - —————————— = 0 5 4

STEP7:

STEP8:

Pulling out like terms :

 8.1     Pull out like factors :

   27y + 12  =   3 • (9y + 4) 

Calculating the Least Common Multiple :

 8.2    Find the Least Common Multiple

The left denominator is :       5 

      The right denominator is :       4