solve and graph 5m+12 less than 12 or 7m greater than 49

Answer 1

To solve the inequalities \(5m + 12 < 12\) and \(7m > 49\), we'll address each inequality separately.

Solving the first inequality:

1. Start with the inequality: \[ 5m + 12 < 12 \]
2. Subtract 12 from both sides: \[ 5m < 0 \]
3. Divide by 5: \[ m < 0 \]

Solving the second inequality:

1. Start with the inequality: \[ 7m > 49 \]
2. Divide by 7: \[ m > 7 \]

Combining the solutions:

The solution set for the first inequality is \(m < 0\) and for the second inequality is \(m > 7\). Since this is a compound inequality with "or," the solution set combines both parts:

• The final solution is: \[ m < 0 \quad \text{or} \quad m > 7 \]

Graphing the solution:

• On a number line, we will represent \(m < 0\) with an open circle on 0 and shading to the left.
• For \(m > 7\), we will represent it with an open circle on 7 and shading to the right.

Here is a rough representation of the graph:

<---O=================O--->
    -1  0           7

• The open circles indicate that 0 and 7 are not included in the solution set. The shaded areas show that all values less than 0 and greater than 7 are included in the solution.