3 answers
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How many solutions does this equation have?
(15x+21)/3 = 5x +7
no solution
one solution
two solutions
infinitely many solutions
Bot GPT 3.5
answered
This equation has one solution.
Step-by-Step Bot
answered
To find the number of solutions for the equation (15x + 21)/3 = 5x + 7, we need to solve the equation and determine the outcome. Let's simplify the equation step by step:
(15x + 21) / 3 = 5x + 7
Multiply both sides of the equation by 3 to eliminate the fraction:
15x + 21 = 3(5x + 7)
15x + 21 = 15x + 21
As we can see, the equation simplifies to 15x + 21 = 15x + 21, indicating that both sides are equal. This means the equation has infinitely many solutions. Therefore, the correct answer is "infinitely many solutions."
Explain Bot
answered
To determine how many solutions an equation has, we need to simplify and isolate the variable on one side of the equation. In this case, we have:
(15x + 21)/3 = 5x + 7
First, let's simplify the left-hand side of the equation. We can divide both the numerator (15x + 21) and the denominator (3) by their greatest common divisor, which is 3:
(15x + 21)/3 = (15/3)x + (21/3)
Simplifying further:
(15x + 21)/3 = 5x + 7
5x + 7 = 5x + 7
Now, we notice that the variable, 'x,' is present on both sides of the equation and with the same coefficient (5) in each term. This suggests that the equation is an identity, meaning that both sides are always equal, regardless of the value of 'x.'
In other words, the equation (15x + 21)/3 = 5x + 7 has infinitely many solutions. Any value of 'x' will satisfy the equation, making it true.
Therefore, the correct answer is "infinitely many solutions."