Question

solve each of the following equations:y-6/2=3-2y/5
$3$
​

Answer 1

Answer:

Rearrange:

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

y-6/2-(3-2*y/533)=0

Step by step solution :

STEP

1

:

y

Simplify ———

533

Equation at the end of step

1

:

6 y

(y - —) - (3 - (2 • ———)) = 0

2 533

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 533 as the denominator :

3 3 • 533

3 = — = ———————

1 533

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 • 533 - (2y) 1599 - 2y

—————————————— = —————————

533 533

Equation at the end of step

2

:

6 (1599 - 2y)

(y - —) - ——————————— = 0

2 533

STEP

3

:

3

Simplify —

1

Equation at the end of step

3

:

(1599 - 2y)

(y - 3) - ——————————— = 0

533

STEP

4

:

Rewriting the whole as an Equivalent Fraction

4.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 533 as the denominator :

y - 3 (y - 3) • 533

y - 3 = ————— = —————————————

1 533

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

(y-3) • 533 - ((1599-2y)) 535y - 3198

————————————————————————— = ———————————

533 533

Equation at the end of step

4

:

535y - 3198

——————————— = 0

533

STEP

5

:

When a fraction equals zero

5.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

535y-3198

————————— • 533 = 0 • 533

533

Now, on the left hand side, the 533 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

535y-3198 = 0

Solving a Single Variable Equation:

5.2 Solve : 535y-3198 = 0

Add 3198 to both sides of the equation :

535y = 3198

Divide both sides of the equation by 535:

y = 3198/535 = 5.978

One solution was found :

y = 3198/535 = 5.978