Question - Solving a Compound Inequality with 'Or'
Solution:
The image shows a compound inequality that consists of two parts connected by "or".The first part of the inequality is:\[ 6 + 7m \leq 6m - 5 \]The second part of the inequality is:\[ 3m - 7 < 5 + 6m \]To solve the first part of the inequality, we will isolate the variable $$ m $$ on one side:\[ 6 + 7m \leq 6m - 5 \]Subtract $$ 6m $$ from both sides:\[ 7m - 6m \leq -5 - 6 \]Combine like terms:\[ m \leq -11 \]Now to solve the second part of the inequality:\[ 3m - 7 < 5 + 6m \]Subtract $$ 3m $$ from both sides:\[ -7 < 5 + 3m \]Subtract $$ 5 $$ from both sides to isolate the variable term:\[ -12 < 3m \]Divide both sides by $$ 3 $$ to solve for $$ m $$:\[ -4 < m \]Now we have two parts to the solution, and since they are connected by "or," we will take the union of the two solutions.The solutions to the compound inequality are:\[ m \leq -11 \quad \text{or} \quad m > -4 \]This means that any $$ m $$ that is less than or equal to -11 or greater than -4 satisfies the original compound inequality.
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