Question

Please show all of the steps to solve the Algebra math problems below.Evaluate the following.|10| = |-4| =Subtract. Write your answer as a fraction in simplest form.5/8 � 3/8 =Subtract.7/8 � 5/6Write your answer as a fraction in simplest form.Multiply.6*(-7/2) =Write your answer in simplest form.Divide. Write your answer as a fraction or mixed number in simplest form.6/5 / (- 12/25) =Evaluate.3 + 4^2 * 2 =Evaluate.2/3 + 5/6 * � =Write your answer in simplest form.Evaluate-16 - 12 / (-4) =Use the distributive property to remove the parentheses.-9(3w � x � 2) =Simplify.-2(w + 2) + 5w =Simplify the following expression.16x^2 + 8 � 10x � 2x^2 � 14x =Evaluate the expression when b = -5 and y = 6b � 9y =Evaluate the expression when y = -3Y^2 + 5y � 4 =Evaluate.(-4)^3 =(-7)^2 =Evaluate. Write your answers as fractions.3/5^3 =(-1/3)^2 =Evaluate the expressions.(-7)^0 =2(1/3)^0 = Multiply.3v^2(-5v^4) =Simplify your answer as much as possible.Multiply.2y^2w^4*6y*2w^8 =Simplify your answer as much as possible.Simplify.(4p^3/3p^7)^-2 =Write your answer using only positive exponents.Simplify.X^-2/x^-3 =Write your answer with a positive exponent only.

Answer 1

Answer: So 5 + x = 8 beacase x is 3

Explanation:

Answer 2

See Explanation

Explanation:

Please note that I'll replace all � with +

1. |10|

This implies the absolute value of 10 and it always returns the positive value;

Hence;

`|10| = 10`

2. |-4|

Using the same law applied in (1)

`|-4| = 4`

3. 5/8 - 3/8 = ?

Take LCM

`= (5 - 3)/(8)`

Subtract the numerator

`= (2)/(8)`

Divide the numerator and denominator by 2

`= (1)/(4)`

Hence:

`(5)/(8) - (3)/(8) = (1)/(4)`

4. 7/8 - 5/6

Take LCM

`= (21 - 20)/(24)`

`= (1)/(24)`

Hence;

`(7)/(8) - (5)/(6) = (1)/(24)`

5. 6 * (-7/2)

`= 6 * (-7)/(2)`

Multiply the numerator

`= (-42)/(2)`

`= -21`

Hence:

`6 * (-7)/(2) = -21`

5. 6/5 /(-12/25)

`= (6)/(5) / (-12)/(25)`

Change the divide to multiplication

`= (6)/(5) * (-25)/(12)`

Divide 6 and 12 by 6

`= (1)/(5) * (-25)/(2)`

Divide 5 and 25 by 5

`= (1)/(1) * (-5)/(2)`

`= (-5)/(2)`

Hence;

`(6)/(5) / (-12)/(25) = (-5)/(2)`

6. 3 + 4^2 * 2

`= 3 + 4^2 * 2`

Solve the exponent

`= 3 + 16 * 2`

Apply B.O.D.M.A.S

`= 3 + 32`

`= 35`

`3 + 4^2 * 2 = 35`

7. 2/3 + 5/6

`= (2)/(3) + (5)/(6)`

Apply LCM

`= (4 + 5)/(6)`

`= (9)/(6)`

Divide the numerator and denominator by 3

`= (3)/(2)`

Convert to mixed fraction

`= 1(1)/(2)`

Hence;

`(2)/(3) + (5)/(6) = 1(1)/(2)`

8. 16 - 12/(-4)

`= 16 - (12)/(-4)`

Solve the fraction

`= 16 - (-3)`

Open the bracket

`= 16 + 3`

`= 19`

Hence;

`16 - (12)/(-4) = 19`

9. -9(3w + x + 2)

`= -9(3w + x + 2)`

Open brackets: Distributive property

`= -9*3w -9* x -9 * 2`

`= -27w -9 x -18`

Hence;

`-9(3w + x + 2) = -27w -9 x -18`

10. -2(w + 2) + 5w

`= -2(w + 2) + 5w`

Open bracket: using distributive property

`= -2*w -2 * 2 + 5w`

`= -2w -4 + 5w`

Collect Like Terms

`= 5w-2w -4`

`= 3w -4`

Hence;

`-2(w + 2) + 5w = 3w- 4`

11. 16x^2 + 8 + 10x + 2x^2 + 14x

`= 16x^2 + 8 + 10x + 2x^2 + 14x`

Collect Like Terms

`= 16x^2 + 2x^2 + 10x + 14x+ 8`

`= 18x^2 + 24x + 8`

Expand the expression

`= 18x^2 + 12x + 12x + 8`

Factorize:

`= 6x(3x + 2) + 4(3x +2)`

`= (6x + 4)(3x +2)`

Hence;

`16x^2 + 8 + 10x + 2x^2 + 14x = (6x + 4)(3x +2)`

12. b = -5 and y = 6

`b + 9y =?`

Substitute -5 for b and 6 for y

`= -5 + 9 * 6`

`= -5 + 54`

`= 49`

Hence;

`b + 9y = 49`

13. y = -3

`y^2 + 5y + 4 =?`

Substitute -3 for y

`= (-3)^2 + 5(-3) + 4`

Open all brackets

`= 9 -15 + 4`

`= -2`

Hence;

`y^2 + 5y + 4 = -2`

14.

`(-4)^3`

Open bracket:

`= -4 * -4 * -4`

`= -64`

Hence;

`(-4)^3 = -64`

`(-7)^2`

Open bracket:

`= -7 * -7`

`= 49`

Hence;

`(-7)^2 = 49`

15. Express as fractions:

`(3)/(5^3)`

Evaluate the denominator

`= (3)/(125)`

Hence:

`(3)/(5^3) = (3)/(125)`

`((-1)/(3))^2`

Evaluate the exponent

`= ((-1)/(3))*((-1)/(3))`

`=(1)/(9)`

Hence:

`((-1)/(3))^2=(1)/(9)`

16. Evaluate

`(-7)^0 =`

Evaluate the exponent

`(-7)^0 = 1`

`2 * (1/3)^0`

Evaluate the exponent

`= 2 * 1`

`= 2`

Hence;

`2 * (1/3)^0 = 2`

17. Evaluate

`3v^2(-5v^4)`

Open bracket

`= 3 * v^2*-5* v^4`

Reorder

`= 3 *-5* v^4 * v^2`

`= -15* v^4 * v^2`

Apply law of indices

`= -15* v^(4 +2)`

`= -15* v^6`

`= -15v^6`

Hence:

`3v^2(-5v^4) = -15v^6`

18.

`2y^2w^4*6y*2w^8`

Rewrite as

`2 *y^2 * w^4*6 * y*2 * w^8`

Reorder the terms

`=2*6 * w^4 * w^8*y^2 * y*2`

`=12 * w^4 * w^8*y^2 * y*2`

Apply law of indices

`=12 * w^(4+8) *y^(2+2)`

`=12 * w^(12) *y^4`

`=12 w^(12) y^4`

Hence:

`2y^2w^4*6y*2w^8 =12 w^(12) y^4`

19.

`((4p^3)/(3p^7))^(-2)`

Apply law of indices

`= ((4p^(3-7))/(3))^(-2)`

`= ((4p^(-4))/(3))^(-2)`

Apply law of indices

`= ((4)/(3p^4))^(-2)`

Apply law of indices

`= ((3p^4)/(4))^(2)`

`= ((3p^4)/(4)) * ((3p^4)/(4))`

Evaluate

`= (9p^8)/(16)`

Hence;

`((4p^3)/(3p^7))^(-2) = (9p^8)/(16)`

20.

`(x^(-2))/(x^(-3))`

Apply law of indices

`= x^(-2 - (-3))`

`= x^(-2 +3)`

`= x^1`

`= x`

Hence:

`(x^(-2))/(x^(-3)) =x`