Question

solve the equation and check your solution.
$7c + 12 = -4c + 78$
$c = \square$
need help?

Explanation:

Step1: Add 4c to both sides

To get all the \( c \)-terms on one side, we add \( 4c \) to both sides of the equation \( 7c + 12 = -4c + 78 \). This gives us \( 7c + 4c + 12 = -4c + 4c + 78 \), which simplifies to \( 11c + 12 = 78 \).

Step2: Subtract 12 from both sides

Next, we isolate the term with \( c \) by subtracting 12 from both sides. So, \( 11c + 12 - 12 = 78 - 12 \), which simplifies to \( 11c = 66 \).

Step3: Divide by 11

Finally, we solve for \( c \) by dividing both sides by 11. \( \frac{11c}{11} = \frac{66}{11} \), so \( c = 6 \).

Step4: Check the solution

Substitute \( c = 6 \) back into the original equation. Left side: \( 7(6) + 12 = 42 + 12 = 54 \). Right side: \( -4(6) + 78 = -24 + 78 = 54 \). Both sides are equal, so the solution is correct.

Answer:

\( c = 6 \)