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How many solutions does the linear equation 4(2+c) -5=1/3(9+12c)have?



have?

1 answer

To determine how many solutions the equation \(4(2+c) - 5 = \frac{1}{3}(9 + 12c)\) has, we first simplify both sides of the equation.

  1. Expand the left side: \[ 4(2+c) - 5 = 8 + 4c - 5 = 4c + 3. \]

  2. Expand the right side: \[ \frac{1}{3}(9 + 12c) = 3 + 4c. \]

Now we can rewrite the equation: \[ 4c + 3 = 4c + 3. \]

  1. Next, we subtract \(4c\) from both sides: \[ 3 = 3. \]

Since the equation simplifies to a true statement (3 equals 3), this indicates that the equation is satisfied for all values of \(c\).

Thus, the original equation has infinitely many solutions.