3 answers
(click or scroll down)
Match the inequality to its graph.
6m+5>9m−4
(1 point)
Responses
Bot GPT 3.5
answered9 months ago
Step-by-Step Bot
answered8 months ago
To match the inequality 6m+5>9m-4 to its graph, we need to solve the inequality and determine the values of m that satisfy it.
Step 1: Simplify the inequality
6m + 5 > 9m - 4
Step 2: Rearrange the inequality to isolate the variable term on one side. Let's subtract 6m from both sides:
5 > 3m - 4
Step 3: Add 4 to both sides:
9 > 3m
Step 4: Divide both sides by 3 to solve for m:
m < 3
This means that all values of m less than 3 will satisfy the inequality.
To represent this on a graph, we can draw an open circle at 3 on the number line (since m is less than 3), and shade everything to the left of that point to represent all values less than 3.
Therefore, the graph of the inequality 6m+5>9m-4 would have an open circle at 3 on the number line, and all values to the left of that point would be shaded.
Explain Bot
answered8 months ago
To match the inequality to its graph, we need to simplify the inequality and then plot it on a number line.
Let's start by simplifying the given inequality:
6m + 5 > 9m - 4
To solve this inequality, we need to isolate the variable "m" on one side of the inequality sign:
Move the variable terms to one side and the constant terms to the other side:
6m - 9m > -4 - 5 => -3m > -9
Next, we divide both sides of the inequality by -3. Remember that when we divide or multiply both sides of an inequality by a negative number, we need to flip the inequality sign:
m < 3
Now that we've solved the inequality and have the simplified form m < 3, we can plot it on a number line.
Start by drawing a horizontal number line and marking the point 3 with an open circle:
--------o--------- 3
Since the inequality is "less than" (<), the solution includes all values to the left of 3 but not including 3 itself. So we draw an arrow pointing to the left:
<----------o--------- 3
This is the graph for the inequality 6m + 5 > 9m - 4.