The table below shows two equations:
Equation 1 |3x - 1| + 7 = 2
Equation 2 |2x + 1| + 4 = 3
Which statement is true about the solution to the two equations?
Equation 1 and equation 2 have no solutions.
Equation 1 has no solution and equation 2 has solutions x = 0, 1.
The solutions to equation 1 are x = -1.3, 2 and equation 2 has no solution.
The solutions to equation 1 are x = -1.3, 2 and equation 2 has solutions x = 0, 1
equation #1:
|3x-1| + 7 = 2
|3x-1| = -5
but by definition, the |anything| cannot be negative,
the same is true for the 2nd equation.
So neither one has a solution
Reiny is incorrect, the answer is D) the last statement
To find the solution to Equation 1, we'll first isolate the absolute value expression:
|3x - 1| + 7 = 2
Subtracting 7 from both sides:
|3x - 1| = -5
Since the absolute value of any expression cannot be negative, Equation 1 has no solutions.
To find the solution to Equation 2, we'll isolate the absolute value expression in the same way:
|2x + 1| + 4 = 3
Subtracting 4 from both sides:
|2x + 1| = -1
Again, the absolute value of any expression cannot be negative, so Equation 2 also has no solutions.
Therefore, the correct statement is:
Equation 1 and equation 2 have no solutions.
To find the solutions to the equations, we need to solve for x in each equation.
Equation 1: |3x - 1| + 7 = 2
To solve this equation, we need to isolate the absolute value term. Let's start by subtracting 7 from both sides:
|3x - 1| = 2 - 7
Simplifying, we get:
|3x - 1| = -5
Absolute values cannot be negative, so the equation has no solution.
Equation 2: |2x + 1| + 4 = 3
Again, we need to isolate the absolute value term. We will start by subtracting 4 from both sides:
|2x + 1| = 3 - 4
Simplifying further, we have:
|2x + 1| = -1
Again, absolute values cannot be negative, so this equation also has no solution.
Therefore, the correct statement is:
Equation 1 and equation 2 have no solutions.