Linear(Simple) Equations: Problems with Solutions

Solution:
By substracting 2 from both sides, we get
n + 2 - 2 = 6 - 2,
or n = 4

Solution:
By adding 5 to both sides, we get z=5+6, or z=11.

Solution:
We add t to both sides of the equation, and we get 5-t+t=0+t, or t=5.

Solution:
By substracting 7 from both sides, we get n+7-7=13-7, or n=6.

Solution:
[tex]x=82-34=48[/tex]

Solution:
By adding a to both sides, we get 3-a+a=2a+a, or 3a=3. The we divide both sides by 3 to reach the final answer, a=1.

Solution:
[tex]2x=10+20[/tex]
[tex]2x=30[/tex]
[tex]x=15[/tex]

Solution:
[tex]20 - 2x = 18[/tex]
[tex]20 - 18 = 2x[/tex]
[tex]2=2x[/tex]
[tex]x=1[/tex]

Solution:
We add 2 to both sides and get 5c-2+2=33+2, or 5c=35. We divide both sides by 5 in order to get c=7.

Solution:
We divide both sides of the equation with 4:
[tex]\frac{4x}{4}=\frac{72}{4}[/tex]
[tex]x=18[/tex]

Solution:
[tex]13x=24+15[/tex]
[tex]13x=39[/tex]
[tex]x=3[/tex]

Solution:
We multiply both sides of the equation by 3 in order to get [tex]\frac{b}{3}\cdot3=3\cdot3[/tex], or b=9.

Solution:
[tex]2x=40-2[/tex]
[tex]2x=38[/tex]
[tex]x=19[/tex]

Solution:
By substracting 1 from both sides, we get 3x+1-1=16-1, or 3x=15. We divide both sides by 3 in order to get the value for x: x=5.

Solution:
By substracting 5 from both sides of the equation, we get 2x+5-5=9-5, or 2x=4. Then we divide both sides by 2 to reach the solution, [tex]x=2[/tex].

Solution:
By substracting m from both sides, we get m+10-m=3m-m, so 10=2m or 2m=10. Dividing both sides of the equation by 2, we find that m=5

Solution:
We divide both sides by 19:
[tex]\frac{19z}{19}=\frac{38}{19}+6\cdot\frac{19}{19}[/tex]
[tex]z=2+6[/tex]
[tex]z=8[/tex]

Solution:
First, we substract 6 from both sides to get 2y+6-6=y+11-6, or 2y=y+5.
Then we substract y from both sides to reach the final solution, y=5.

Solution:
The equation is defined for [tex]x \ne 0[/tex]. We cross multiply and get
[tex]x=5[/tex], which is a valid value for x and the solution.

Solution:
[tex]x+x+x-1-2-3=0[/tex]
[tex]3x-6=0[/tex]
[tex]3x=6[/tex]
[tex]x=2[/tex]

Solution:
[tex]10+74=13y-y[/tex]
[tex]12y=84[/tex]
[tex]y=7[/tex]

Solution:
We substract 3c from both sides of the equation to get 3c-3c=8c-3c, or 5c=0. The we divide both sides by 5 and the answer is c=0.

Solution:
First we multiply both sides by 8 to get free of the denominator. That yields [tex]\frac{3}{8}a\cdot8=3\cdot8[/tex], or 3a=24. Then we divide both sides by 3 to get a=8.

Solution:
4x-9=2x+7
2x=16
x=16/2
x=8

Solution:
[tex]5x-3x=-24-12[/tex]
[tex]2x=-36[/tex]
[tex]x=-18[/tex]

Solution:
We multiply both sides by 5: [tex]5\cdot\frac{x}{5}=8\cdot5[/tex] in order to get x=40.

Solution:
We substract on the right side: 28=7y. Then we divide by 7 in order to get the solution, y=4.

Solution:
-2х = 2 + 6
-2х = 8
х= -8 : 2
х= -4

Solution:
19 + 19x = 3x - 9
19x - 3x= -9 - 19
+16x = -28
x= -28 ÷ 16
x= -1.75 or -7/4

Solution:
x + 7 = 16
x = 16 - 7
x = 9
8x - 72 = 8 × 9 - 72 = 72 - 72=0

Solution:
Subtract 3x from both sides of the equation.
3x + 3 - 3x = 7x - 9 - 3x
3 = 4x - 9
Add 9
3 + 9 = 4x - 9 + 9
12 = 4x
Divide by 4
3 = x

Solution:
Let the number be x.

Then the other number = x + 9

Sum of two numbers = 45

According to the question, x + (x + 9) = 45

⇒ 2x + 9 = 45

⇒ 2x = 45 - 9 (transposing 9 to the R.H.S changes to -9)

⇒ 2x = 36

⇒ 2x/2 = 36/2 (divide by 2 on both the sides)

⇒ x = 18

Therefore, x + 9 = 18 + 9 = 27

Therefore, the two numbers are 18 and 27.