Question

1. Give a brief explanation as to what kind of solution(s) you expect for the

linear equation 18x + ½ = 6(3x + 25). Transform the equation into a simpler
form if necessary.
2. Give a brief explanation as to what kind of solution(s) you expect for the
linear equation 8-9x = 15x + 7 + 3x. Transform the equation into a simpler
form if necessary.
3. Give a brief explanation as to what kind of solution(s) you expect for the
linear equation 5(x + 9) = 5x + 45. Transform the equation into a simpler
form if necessary.
4. Give three examples of equations where the solution will be unique; that is,
only one solution is possible.
a. Equation 1.
b. Equation 2
c. Equation 3
5. Solve one of the equations you wrote in Problem 4, and explain why it is the
only solution.
6. Give three examples of equations where there will be no solution..
a. Equation 1
b. Equation 2
c. Equation 3

Answer 1

1. No solutions

2. x = 1/27

3. Solution: all real numbers

4.

Explanation:

(1) 18x + 1/2 = 6(3x + 25)

18x + 12 = 18x + 150

18x = 18x + 150 - 12

18x - 18x = 138

0 is not = 138

No solutions

(2) 8-9x = 15x + 7 + 3x

8 - 7 = 15x + 3x + 9 x

1 = 27x

x = 1/27

(3). 5(x+9) = 5x + 45

5x + 45 = 5x + 45

5x - 5x = 45 - 45

0=0

All real numbers are solution.

(4) Equations with one variable have one solution.

a. 3x + 6 = 9

b. 2x - 6 = -4

c. 8x + 2 = 10

(5) 3x + 6 = 9

3x = 9 - 6

x = 3/3

x = 1 is the only solution

3(1) + 6 = 9

9 = 9

(6) a. 6x + 2 = 6x

b. 2x + 5 + 3x = 5x

c. 14 - 6x = -6x