does 3(4x+8)=4(3x+6) have Infinite solutions
No, the equation does not have infinite solutions. The equation simplifies to 12x + 24 = 12x + 24, and when we subtract 12x and 24 from both sides of the equation, we get 0 = 0. This means that the equation is an identity, which means that the equation is true for any value of x. Therefore, the equation has infinite solutions.
To determine if the equation 3(4x+8)=4(3x+6) has infinite solutions, we need to compare the terms on both sides of the equation and simplify.
Step 1: Distribute the coefficients to the terms within the parentheses on both sides.
3 * 4x + 3 * 8 = 4 * 3x + 4 * 6
12x + 24 = 12x + 24
Step 2: Observe that the equation simplifies to 12x + 24 = 12x + 24, which, at first glance, appears to mean that the equation has no solution. However, we need to dig deeper.
Step 3: Notice that the variable term (12x) appears on both sides of the equation. Since the variable term is the same on both sides, it means that the equation is an identity. An identity is always true, regardless of the value of the variable. Therefore, this equation has infinite solutions.
In conclusion, the equation 3(4x+8)=4(3x+6) does have infinite solutions.
To determine if the equation 3(4x+8) = 4(3x+6) has infinite solutions, we need to simplify and see if the simplified equation is always true, regardless of the value of x.
Step 1: Distribute the values inside the parentheses.
3(4x+8) becomes 12x + 24
4(3x+6) becomes 12x + 24
Step 2: Rewrite the simplified equation.
12x + 24 = 12x + 24
The equation 12x + 24 = 12x + 24 is always true, regardless of the value of x. This means that any value of x would satisfy the equation.
Therefore, the given equation 3(4x+8) = 4(3x+6) has infinite solutions.