Question

solve each equation if there is no solution write no solution if every number works write all real numbers.1. 6x-16=14x+82. 9y+21=3y-53. 5n+7+3n=-8+3n 4. 6d-1=-d+ 205. 3b+8-5b= 2 (4-b)6. -11 - 2p= 6p+5 (p+3)7. 7w-3 (w+6) = 6w+ 148. 6(n+3)=2 (3n-9)9. -(3b-15)=6 (2b+5)10. h+3 (h-2)=2 (2h-3)11. 5m+6-3m-9=4 (m-3)12. 4(x-2)= 8 (x-3)- 12

Answer 1

1.

6x - 16 = 14x + 8

the question above can be solved by simply collecting like terms and solve for x

step 1

collect like terms by carrying 6x to the right hand side and taking 8 to the left hand side

however, note that the sign changes when they cross equality sign

`\begin{gathered} 6x-16=14x+8 \\ \text{collect like terms} \\ -16-8=14x-6x \\ -24=8x \end{gathered}`

proceed to divide both sides by 8 to solve for x

`\begin{gathered} 8x=-24 \\ (8x)/(8)=(-24)/(8) \\ x=-3 \end{gathered}`

2.

9y + 21 = 3y - 5

step 1

collect like terms

`\begin{gathered} 9y+21=3y-5 \\ 9y-3y=-5+21 \\ 6y=16 \\ \end{gathered}`

step 2

divide both sides by 6

`\begin{gathered} (6y)/(6)=(16)/(6) \\ y=(8)/(3) \end{gathered}`

3

5n + 7 + 3n = -8 + 3n

step 1

`\begin{gathered} 5n+3n-3n=-8-7 \\ 5n=-15 \\ n=(-15)/(5) \\ n=-3 \end{gathered}`

4

6d - 1 = -d + 20

`\begin{gathered} 6d+d=20+1 \\ 7d=21 \\ (7d)/(7)=(21)/(7) \\ d=3 \end{gathered}`

5

3b + 8 - 5b = 2(4 - b)

step 1

open the bracket on the right hand side and collect like terms

`\begin{gathered} 3b+8-5b=8-2b \\ 8-8=-2b+5b-3b \\ 0=0 \end{gathered}`

6

-11 - 2p = 6p + 5(p + 3)

-11 - 2p = 6p + 5p + 15

`\begin{gathered} -11-15=6p+5p+2p \\ -26=13p \\ (13p)/(13)=(-26)/(13) \\ p=-2 \end{gathered}`

10

h + 3(h - 2) = 2(2h -3)

step 1

simplify by opening the bracket

`\begin{gathered} h+3(h-2)=2(2h-3) \\ h+3h-6=4h-6 \\ 4h-4h=-6+6 \\ 0=0 \end{gathered}`

7

7w - 3(