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We are tasked with finding the lowest integer value that \( m \) can take, given the inequality:

\[
7m + 5 > 49 - 3m
\]

### Step 1: Isolate \( m \)
Start by moving all terms involving \( m \) to one side and constant terms to the other.

Add \( 3m \) to both sides:

\[
7m + 3m + 5 > 49
\]

Simplifying:

\[
10m + 5 > 49
\]

### Step 2: Eliminate the constant term
Subtract 5 from both sides:

\[
10m > 44
\]

### Step 3: Solve for \( m \)
Now, divide both sides by 10:

\[
m > 4.4
\]

### Step 4: Find the lowest integer
The lowest integer greater than 4.4 is 5.

### Conclusion:
The lowest integer value that \( m \) can take is \( \boxed{5} \).

Would you like further details on this solution or have any questions?

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Here are some follow-up questions you might find helpful:
1. What happens to the inequality if the signs of the coefficients change?
2. How would the solution change if \( m \) had to be less than a certain value?
3. What if the inequality was \( 7m + 5 \geq 49 - 3m \)? How would this affect the result?
4. Can you solve a similar inequality but with fractions instead of whole numbers?
5. How would you approach solving this inequality graphically?

**Tip:** Always check your final solution by substituting it back into the original inequality to ensure it satisfies the condition.

Work out the lowest integer value that m can take if 7m + 5 > 49 - 3m

Find the lowest integer value that satisfies the inequality 7m + 5 > 49 - 3m. This solution includes a step-by-step breakdown suitable for students in Grades 7-9, covering key algebra concepts like inequalities and linear equations.

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