Question

linear equations and linear systems
problem 1: here is an equation: 2x = 8 + 6
how many solutions does this equation have? circle your answer.
no solution one solution infinite solutions
show your work/explain your reasoning:
2x = 8 + 6

problem 2: here is an equation: 12x + 9 - 4x + 3 = 17 + 8x - 5
how many solutions does this equation have?
no solution one solution infinite solutions
show your work/explain your reasoning:
12x + 9 - 4x + 3 = 17 + 8x - 5

Explanation:

Problem 1

Step1: Simplify right-hand side

$2x = 14$

Step2: Isolate $x$ by dividing by 2

$x = \frac{14}{2} = 7$

Problem 2

Step1: Combine like terms on left

$12x - 4x + 9 + 3 = 8x + 12$

Step2: Combine like terms on right

$17 - 5 + 8x = 8x + 12$

Step3: Subtract $8x$ from both sides

$12 = 12$ is false, so no solution.

Answer:

Problem 1: One Solution
Problem 2: No Solution