Question

A)3x+14=5x-24 b)12x-10x-14=120c) (14-5x)-(8-10x)=102d)6(x-8)=5(x-8)e)5(2c-2)-6(3c-12)=18f)12(18-3y)=180

Answer 1

a)3x-5x=-24-14

    -2x=-38

      x=19

b)12x-10x=120+14

    2x=134

     x=67

c)14-5x-8+10x=102

    -5x+10x=102-14+8

      5x=96

       x=19.2

d)6x-48=5x-40

   6x-5x=-40+48

    x=8

e)10c-10-18c+72=18

   10c-18c=18-10-72

    -8c=-64

    c=8

f)216-36y=180

    -36y=180-216

    -36y=-36

     y=1

 

Answer 2

Let's solve each equation step by step:

a) 3x + 14 = 5x - 24

First, let's simplify the equation by moving all the terms with x to one side:

3x - 5x = -24 - 14

-2x = -38

Now, divide both sides by -2 to solve for x:

x = (-38) / (-2)

x = 19

So the solution to this equation is x = 19.

b) 12x - 10x - 14 = 120

Combine like terms on the left side:

2x - 14 = 120

Next, move the constant term to the right side by adding 14 to both sides:

2x = 120 + 14

2x = 134

Divide both sides by 2:

x = 134 / 2

x = 67

So the solution to this equation is x = 67.

c) (14 - 5x) - (8 - 10x) = 102

First, let's simplify the equation by removing the parentheses:

14 - 5x - 8 + 10x = 102

Combine like terms:

(10x - 5x) + (14 - 8) = 102

5x + 6 = 102

Next, move the constant term to the right side by subtracting 6 from both sides:

5x = 102 - 6

5x = 96

Divide both sides by 5:

x = 96 / 5

So the solution to this equation is x = 19.2.

d) 6(x - 8) = 5(x - 8)

First, distribute the 6 and 5 to the terms inside the parentheses:

6x - 48 = 5x - 40

Next, move all terms with x to one side:

6x - 5x = -40 + 48

x = 8

So the solution to this equation is x = 8.

e) 5(2c - 2) - 6(3c - 12) = 18

First, distribute the 5 and 6 to the terms inside the parentheses:

10c - 10 - 18c + 72 = 18

Combine like terms:

(10c - 18c) + (-10 + 72) = 18

-8c + 62 = 18

Next, move the constant term to the right side by subtracting 62 from both sides:

-8c = 18 - 62

-8c = -44

Divide both sides by -8:

c = (-44) / (-8)

c = 5.5

So the solution to this equation is c = 5.5.

f) 12(18 - 3y) = 180

First, distribute the 12 to the term inside the parentheses:

216 - 36y = 180

Next, move the constant term to the right side by subtracting 216 from both sides:

-36y = 180 - 216

-36y = -36

Divide both sides by -36:

y = (-36) / (-36)

y = 1

So the solution to this equation is y = 1.