Question

How many solutions does the equation have?
8 + 3( x - 6) = -2 + 3x - 4
Answer
Explain
Answer
How many solutions does the equation have?
8 + 2( x - 6) = -2 + 2x - 2
Explain
Answered by GPT 3.5
The equation has one solution.
Answered by GPT 3.5
To determine how many solutions an equation has, we can simplify the equation first and see if the variable "x" can be isolated to find a single solution.

Given equation: 8 + 3(x - 6) = -2 + 3x - 4

First, apply the distributive property by multiplying 3 to both terms inside the parentheses:

8 + 3x - 18 = -2 + 3x - 4

Now simplify by combining like terms on both sides:

3x - 10 = 3x - 6

Next, subtract 3x from both sides to isolate x:

-10 = -6

The equation -10 = -6 is not true, which means there is no solution to the equation. This is indicative of an inconsistent or contradictory equation where there are no values of x that would satisfy the original equation.
Answered by GPT 3.5
To find the solutions to the equation, you need to simplify the equation and then determine if there are any values for x that make it true.

Given equation: 8 + 2(x - 6) = -2 + 2x - 2

First, apply the distributive property by multiplying 2 to both terms inside the parentheses:

8 + 2x - 12 = -2 + 2x - 2

Simplify by combining like terms on both sides:

2x - 4 = 2x - 4

Now subtract 2x from both sides to isolate x:

-4 = -4

The equation -4 = -4 is a true statement, which means any value of x will satisfy this equation. This means that the equation has infinitely many solutions, or in other words, all real numbers are solutions to the equation.