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Given $\frac{2x}{ 3} + \frac{5}{7} = \frac{6x }{ 7}$ - 3

**Step 1:**

The given equation has denominators that need to be cleared by multiplying all terms of the equation by the lowest common denominator.

LCD of the denominators 3 and 7 = 21

21($\frac{2x}{ 3} + \frac{5}{7}$) = 21($ \frac{6x }{ 7}$ - 3)

=> $\frac{2x * 21}{ 3} + \frac{5 * 21}{7}$ = $ \frac{6x * 21}{ 7 }$ - 3 * 21

=> 7 * 2x + 3 * 5 = 3 * 6x - 21 * 3

=> 14x + 15 = 18x - 63

**Step 2:**

Solve for x,

=> 18x - 14x = 63 + 15

=> 4x = 78

Divide each side by 4

=> $\frac{4x}{4} = \frac{78}{4}$

=> x = 19 . 5**answer**

The given equation has denominators that need to be cleared by multiplying all terms of the equation by the lowest common denominator.

LCD of the denominators 3 and 7 = 21

21($\frac{2x}{ 3} + \frac{5}{7}$) = 21($ \frac{6x }{ 7}$ - 3)

=> $\frac{2x * 21}{ 3} + \frac{5 * 21}{7}$ = $ \frac{6x * 21}{ 7 }$ - 3 * 21

=> 7 * 2x + 3 * 5 = 3 * 6x - 21 * 3

=> 14x + 15 = 18x - 63

Solve for x,

=> 4x = 78

Divide each side by 4

=> $\frac{4x}{4} = \frac{78}{4}$

=> x = 19 . 5

Given 10x^{2} + 20x - 80

Given polynomial is quadratic polynomial

Solve for x,

Factorized the polynomial

=> 10x^{2} + 20x - 80 = 10x^{2} + 40x - 20x - 80

= 10x(x + 4) - 20(x + 4)

= (10x - 20)(x + 4)

=> 10x^{2} + 20x - 80 = (10x - 20)(x + 4). **answer**

Given polynomial is quadratic polynomial

Solve for x,

Factorized the polynomial

=> 10x

= 10x(x + 4) - 20(x + 4)

= (10x - 20)(x + 4)

=> 10x

Let the two numbers be x and y.

also y is smaller than x (y < x).

Step 1:

Given sum of two numbers is 70

=> x + y = 70 .......................................(1)

and one number is six less than the other number

=> y = x - 6 .........................................(2)

**Step 2: **

Solve equation (1) and equation (2)

Substitute equation (2) in (1)

=> x + (x - 6) = 70

=> x + x - 6 = 70

=> 2x - 6 = 70

Add 6 both sides

=> 2x - 6 + 6 = 70 + 6

=> 2x = 76

Divide each side by 2

=> $\frac{2x}{2} = \frac{76}{2}$

=> x = 38

**Step 3: **

Put x = 38 in equation (2)

=> y = 38 - 6

=> y = 32

Hence the smaller number is 32.**answer**

also y is smaller than x (y < x).

Step 1:

Given sum of two numbers is 70

=> x + y = 70 .......................................(1)

and one number is six less than the other number

=> y = x - 6 .........................................(2)

Solve equation (1) and equation (2)

Substitute equation (2) in (1)

=> x + (x - 6) = 70

=> x + x - 6 = 70

=> 2x - 6 = 70

Add 6 both sides

=> 2x - 6 + 6 = 70 + 6

=> 2x = 76

Divide each side by 2

=> $\frac{2x}{2} = \frac{76}{2}$

=> x = 38

Put x = 38 in equation (2)

=> y = 38 - 6

=> y = 32

Hence the smaller number is 32.