Question

~~~ 30 POINTS ~~~

Directions: Write an equation to represent each relationship. Then solve the equation.

1. Two less than 3 times a number is the same as the number plus 10.
2. A number increased by 4 is the same as 19 minus 2 times the number.
3. Twenty less than 8 times a number is the same as 15 more than the number.

Answer 1

let x be the unknown number of all 3 equations
1.) 3x - 2 = x + 10 x=6
2.) x + 4 = 19 - 2x x=5
3.) 8x - 20 = x + 15 x=5

Answer 2

1) 3x-2=x+10


Now, lets solve this step-by-step.

3x - 2 = x + 10
-x -x

3x - x = 2x 2x - 2 = 10

2x - 2 = 10
2x - 2+2 = 10+2 The inverse operation helps isolate the variable.

2x = 12

2x/2 = 12/2

x = 12/2
x = 6

Answer: x = 6

2) x + 4 = 19 - 2x

We can solve this much faster

x + 4 = 19 - 2x
+2x

x+2x = 3x

3x + 4 = 19
-4 -4

19-4 = 15

3x= 15
3x/3 = 15/3
x= 5

Answer: x = 5

3) 8x - 20 = x + 15

Much faster now!!

8x - 20 = x + 15
-x
8x-x = 7x

7x - 20 = 15
+20 +20
15+20 = 35

7x = 35
7x/7 = 35/7
x = 35/7
x = 5

Answer: x= 5