Question

1)-7x-40=3x 2)10n-9=7n=12 3)14=2y-2 4)-10z+75=-5z 5)15+4y=y 6)24-15m=15-14m 7)6x+5=7x+3 8)28=7n-7 9)17-12n=3n-13 10)8y-15=7y-12 11)11m-13=15-3m 12)30-15z=40-14z

Answer 1

1)-7х-40=3х
-7х-3х=40
-10х=40
х=40:(-10)
х=-4
2)10n-9=7n-12
10n-7n=9-12
3n=-3
n=-3:3
n=-1
3)14=2y-2
-2y=-14-2
-2y=-16
y=-16:(-2)
y=8
4)-10z+75=-5z
-10z+5z=-75
-5z=-75
z=-75:(-5)
z=15
5)15+4y=y
4y-y=-15
3y=-15
y=-15:3
y=-5
6)24-15m=15-14m
-15m+14m=-24+15
-m=-9
m=9
7)6x+5=7x+3
6x-7x=-5+3
-x=-2
x=2
8)28=7n-7
-7n=-28-7
-7n=-35
n=-35:(-7)
n=5
9)17-12n=3n-13
-12n-3n=-17-13
-15n=-30
n=-30:(-15)
n=2
10)8y-15=7y-12
8y-7y=15-12
y=3
11)11m-13=15-3m
11m+3m=13+15
14m=28
m=28:14
m=2
12)30-15z=40-14z
-15z+14z=-30+40
-z=10
z=-10

Answer 2

To solve each equation, we'll isolate the variable on one side of the equation. Let's go through each one step-by-step:

1. -7x - 40 = 3x

Add 7x to both sides: -7x + 7x - 40 = 3x + 7x -40 = 10x

Divide both sides by 10 to find x: x = -40/10 x = -4

2. 10n - 9 = 7n + 12

Subtract 7n from both sides: 10n - 7n - 9 = 7n - 7n + 12 3n - 9 = 12

Add 9 to both sides: 3n - 9 + 9 = 12 + 9 3n = 21

Divide both sides by 3 to find n: n = 21/3 n = 7

3. 14 = 2y - 2

Add 2 to both sides: 14 + 2 = 2y - 2 + 2 16 = 2y

Divide both sides by 2 to find y: y = 16/2 y = 8

4. -10z + 75 = -5z

Add 5z to both sides: -10z + 5z + 75 = -5z + 5z 75 = 0z

Any number multiplied by 0 is 0. Therefore, the equation has no solution for z.

5. 15 + 4y = y

Subtract y from both sides: 15 + 4y - y = y - y 15 + 3y = 0

Subtract 15 from both sides: 15 + 3y - 15 = 0 - 15 3y = -15

Divide both sides by 3 to find y: y = -15/3 y = -5

6. 24 - 15m = 15 - 14m

Add 14m to both sides: 24 - 15m + 14m = 15 - 14m + 14m 24 - m = 15

Subtract 24 from both sides: 24 - m - 24 = 15 - 24 -m = -9

Multiply both sides by -1 to find m: m = 9

7. 6x + 5 = 7x + 3

Subtract 6x from both sides: 6x - 6x + 5 = 7x - 6x + 3 5 = x + 3

Subtract 3 from both sides: 5 - 3 = x + 3 - 3 2 = x

8. 28 = 7n - 7

Add 7 to both sides: 28 + 7 = 7n - 7 + 7 35 = 7n

Divide both sides by 7 to find n: n = 35/7 n = 5

9. 17 - 12n = 3n - 13

Add 12n to both sides: 17 - 12n + 12n = 3n - 13 + 12n 17 = 15n - 13

Add 13 to both sides: 17 + 13 = 15n - 13 + 13 30 = 15n

Divide both sides by 15 to find n: n = 30/15 n = 2

10. 8y - 15 = 7y - 12

Subtract 7y from both sides: 8y - 7y - 15 = 7y - 7y - 12 y - 15 = -12

Add 15 to both sides: y - 15 + 15 = -12 + 15 y = 3

11. 11m - 13 = 15 - 3m

Add 3m to both sides: 11m - 3m - 13 = 15 - 3m + 3m 8m - 13 = 15

Add 13 to both sides: 8m - 13 + 13 = 15 + 13 8m = 28

Divide both sides by 8 to find m: m = 28/8 m = 7/2 or 3.5

12. 30 - 15z = 40 - 14z

Add 14z to both sides: 30 - 15z + 14z = 40 - 14z + 14z 30 - z = 40

Subtract 30 from both sides: 30 - z - 30 = 40 - 30 -z = 10

Multiply both sides by -1 to find z: z = -10

In the equations you provided, some of them have no solution for the variable (e.g., #4), and some have one unique solution (e.g., #1, #2, #3, #5, #6, #7, #8, #9, #10, #12). Equation #11 has a solution, but it is in the form of a fraction (3.5).