Final answer:
In the equation 24x + 12 = 6(4x + a), it will have an infinite number of solutions when the constant 'a' is equal to 2.
Step-by-step explanation:
In the given equation, 24x + 12 = 6(4x + a), for the equation to have an infinite number of solutions, the left hand side (LHS) and the right hand side (RHS) of the equation should be identical. That means, the terms present in LHS and RHS should be equal.
Expressing the RHS, 6(4x + a) becomes 24x + 6a.
For the equation to hold true we need to compare the coefficients on both sides, where:
- Co-efficient of x in LHS is 24, which is equal to the co-efficient of x in RHS, also 24.
- The 12 in the LHS must be equal to 6a in the RHS.
So, 12 = 6a.
To solve for a, divide both sides by 6 and we find that a = 12/6 = 2. Hence, the equation will have an infinite number of solutions when a = 2.
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