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Solve the following inequality:

[tex]\[
\begin{array}{l}
4m + 6 \ \textless \ 2 \text{ OR } \frac{m + 4}{3} \ \textgreater \ 3 \\
m \ \textless \ [?] \text{ OR } m \ \textgreater \ [?]
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
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