Let's solve the inequalities step by step.
### First Inequality: [tex]\(4m + 6 < 2\)[/tex]
1. Isolate the term involving [tex]\(m\)[/tex]:
[tex]\[ 4m + 6 < 2 \][/tex]
2. Subtract 6 from both sides to isolate the [tex]\(4m\)[/tex] term:
[tex]\[ 4m + 6 - 6 < 2 - 6 \][/tex]
[tex]\[ 4m < -4 \][/tex]
3. Divide both sides by 4 to solve for [tex]\(m\)[/tex]:
[tex]\[ m < -1 \][/tex]
So, the solution to the first inequality is:
[tex]\[ m < -1 \][/tex]
### Second Inequality: [tex]\(\frac{(m+4)}{3} > 3\)[/tex]
1. Isolate the fraction:
[tex]\[ \frac{m + 4}{3} > 3 \][/tex]
2. Multiply both sides by 3 to clear the fraction:
[tex]\[ m + 4 > 9 \][/tex]
3. Subtract 4 from both sides to solve for [tex]\(m\)[/tex]:
[tex]\[ m + 4 - 4 > 9 - 4 \][/tex]
[tex]\[ m > 5 \][/tex]
So, the solution to the second inequality is:
[tex]\[ m > 5 \][/tex]
### Combined Solution
The final solution to the given set of inequalities is:
[tex]\[ m < -1 \quad \text{OR} \quad m > 5 \][/tex]
Hence, the values for [tex]\(m\)[/tex] are:
[tex]\[ m < -1 \quad \text{OR} \quad m > 5 \][/tex]
