Question

1. $3x = 2x + 50$ 2) $6x = 2x + 44$ 3) $8x = 2x + 36$ 4) $4x = x + 18$ 5) $7x + 10 = 3x + 120$ 6) $20 + 2x = x + 56$ 7) $6x + 16 = 2x + 28$ 8) $12x + 12 = 3x + 84$ 9) $3 + 6x = 2x + 27$ 10) $8x + 2 = 72 + x$ 11) $2x + 20 = x + 60$ 12) $4x + 1 = 25 + 2x$

Explanation:

Step1: Isolate x - terms for 1)

Subtract 2x from both sides of $3x = 2x + 50$. We get $3x-2x=2x + 50-2x$, so $x = 50$.

Step2: Isolate x - terms for 2)

Subtract 2x from both sides of $6x=2x + 44$. We have $6x-2x=2x + 44-2x$, then $4x=44$, and $x = 11$.

Step3: Isolate x - terms for 3)

Subtract 2x from both sides of $8x=2x + 36$. So $8x-2x=2x + 36-2x$, $6x=36$, and $x = 6$.

Step4: Isolate x - terms for 4)

Subtract x from both sides of $4x=x + 18$. We obtain $4x-x=x + 18-x$, $3x=18$, and $x = 6$.

Step5: Isolate x - terms for 5)

Subtract 3x from both sides of $7x + 10=3x + 120$. We get $7x-3x+10=3x-3x + 120$, $4x+10=120$. Then subtract 10 from both sides: $4x=110$, and $x = 27.5$.

Step6: Isolate x - terms for 6)

Subtract x from both sides of $20 + 2x=x + 56$. So $20+2x-x=x - x+56$, $20 + x=56$, and $x = 36$.

Step7: Isolate x - terms for 7)

Subtract 2x from both sides of $6x+16=2x + 28$. We have $6x-2x+16=2x-2x + 28$, $4x+16=28$. Then subtract 16 from both sides: $4x=12$, and $x = 3$.

Step8: Isolate x - terms for 8)

Subtract 3x from both sides of $12x + 12=3x + 84$. So $12x-3x+12=3x-3x + 84$, $9x+12=84$. Then subtract 12 from both sides: $9x=72$, and $x = 8$.

Step9: Isolate x - terms for 9)

Subtract 2x from both sides of $3 + 6x=2x + 27$. We get $3+6x-2x=2x-2x + 27$, $3 + 4x=27$. Then subtract 3 from both sides: $4x=24$, and $x = 6$.

Step10: Isolate x - terms for 10)

Subtract x from both sides of $8x+2=72 + x$. So $8x-x+2=x - x+72$, $7x+2=72$. Then subtract 2 from both sides: $7x=70$, and $x = 10$.

Step11: Isolate x - terms for 11)

Subtract x from both sides of $2x+20=x + 60$. We have $2x-x+20=x - x+60$, $x+20=60$, and $x = 40$.

Step12: Isolate x - terms for 12)

Subtract 2x from both sides of $4x + 1=25+2x$. So $4x-2x+1=2x-2x + 25$, $2x+1=25$. Then subtract 1 from both sides: $2x=24$, and $x = 12$.

Answer:

1. $x = 50$
2. $x = 11$
3. $x = 6$
4. $x = 6$
5. $x = 27.5$
6. $x = 36$
7. $x = 3$
8. $x = 8$
9. $x = 6$
10. $x = 10$
11. $x = 40$
12. $x = 12$