Solve the equation and check the solution. Express numbers as integers or simplified fractions.5-(M-4)+5M+3=M+12\)

Let's solve the given equation:
\[
5 - (M - 4) + 5M + 3 = M + 12
\]

### Step 1: Distribute the negative sign through the parentheses
\[
5 - M + 4 + 5M + 3 = M + 12
\]

### Step 2: Combine like terms on the left-hand side
\[
(5 + 4 + 3) + (5M - M) = M + 12
\]
\[
12 + 4M = M + 12
\]

### Step 3: Rearrange the equation to isolate terms involving \(M\) on one side
\[
4M - M = 12 - 12
\]
\[
3M = 0
\]

### Step 4: Solve for \(M\)
\[
M = 0
\]

### Step 5: Check the solution by substituting \(M = 0\) back into the original equation
\[
5 - (0 - 4) + 5(0) + 3 = 0 + 12
\]
\[
5 - (-4) + 0 + 3 = 12
\]
\[
5 + 4 + 3 = 12
\]
\[
12 = 12
\]

The solution checks out, so the answer is:
\[
M = 0
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. What happens if you isolate \(M\) first in a different equation?
2. How would the solution change if the constant on the right side was different?
3. Can you explain the importance of checking your solution?
4. What other methods can you use to solve linear equations?
5. How do you handle fractions when solving similar equations?

**Tip:** Always distribute negative signs carefully when dealing with parentheses to avoid mistakes!

Solve the equation and check the solution. Express numbers as integers or simplified fractions. 5 - (M - 4) + 5M + 3 = M + 12

Discover how to solve the linear equation 5 - (M - 4) + 5M + 3 = M + 12 with a detailed, step-by-step solution. This problem explains key algebraic concepts such as distributing terms, combining like terms, and isolating variables. Suitable for students in Grades 6-8.

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