Maths questions help please?

Question

whats the answer to these?

1) 4x+5=3x=26
2) 3x=15-2x
3) 8p-7=6p+3
4) 5(x+2)=2x+16
5) 3(x+2)+2(x+1)=23
6) 8(x+2)=3(x+7)

Many Thanks:)

Answer 1

2) 3x = 15 -2x

Add 2x to each side

3x + 2x = 15 - 2x + 2x

By additive inverse property - a + a = 0

3x + 2x = 15

5x = 15 ( 3x + 2x = 5x)

Divide by 5 each side

x = 15/5

x = 3

 

Answer 2

3) 8p - 7 = 6p + 3

Subtracting 6p + 3 from each side

8p - 7 - ( 6p + 3 ) = 6p + 3 - ( 6p  + 3 ) 

By additive inverse property  - a + a = 0

8p -7 - 6p - 3 = 0  ( - ( a+ b) = - a - b)

2p - 10 = 0  ( 8p - 6p = 2p , -7 - 3 =-10)

Add 10 to each side

2p = 10

Divide by 2 each side

p = 10 / 2

p =  5

Answer 3

4) 5( x + 2) = 2x + 16

Distribute terms using distribution property : a (b+ c) = ab + ac

5*x + 5*2 = 2x + 16

5x + 10 = 2x + 16

Substract 2x + 16 from each side

5x + 10 - (2x + 16) = 2x + 16 - ( 2x + 16 )

5x + 10 - 2x - 16 = 0   ( - (a + b) = -a- b  , -a + a = 0 )

5x - 2x + 10 - 16 = 0

3x - 6 = 0

Add 6 to each side

3x = 6

Divide by 3 each side

x =  6/3

x = 2

Answer 4

6) 8 (x + 2) = 3 (x + 7)

Distribute terms using distribution property : a( b + c) = ab + ac

8*x + 8*2 = 3*x + 3*7

8x + 16 = 3x + 21

Subtract 3x + 21 from each side

8x + 16 - (3x + 21) = 3x + 21 - ( 3x + 21)

By additive inverse property - a + a =0

8x + 16 - 3x - 21 = 0  ( - (a + b) = - a -b)

8x - 3x + 16 - 21 = 0 

5x - 5 = 0

Add 5 to each side

5x = 5

Divide by 5 each side

x = 5/5

x= 1

 

 

Answer 5

5) 3(x + 2) + 2(x + 1) = 23

Distribute terms using distribution property : a( b + c) = ab + ac

 3*x + 3*2 + 2*x + 2*1 = 23

3x + 6 + 2x + 2 = 23

3x + 2x + 6 + 2 = 23

Adding common terms

5x + 8 = 23

Subtract 8 from each side

5x = 23 - 8

5x = 15

Divide each side by 5

x = 15/ 5

x = 3

Answer 6

1) if the equation 4x + 5 = 3x - 26

Separate the variables and constants.

4x - 3x = - 26 - 5

x = - 31

Solution x = - 31.

If the equation is 4x + 5 - 3x = 26

Separate the variables and constants by substracting 5 from each side.

4x - 3x = 26 - 5

x = 26 - 5

x = 21

Solution x = 21.