Match the inequality to its graph.
3−2(x+4)≤5
First, let's simplify the inequality:
3-2(x+4) ≤5
3-2x-8 ≤5
-2x-5 ≤5
-2x-5+5 ≤5+5
-2x ≤10
-2x/(-2) ≥ 10/(-2)
x ≥ -5
The graph of this inequality is a number line with a closed circle at -5 and shading to the right.
To match the inequality 3−2(x+4)≤5 to its graph, we need to first simplify the inequality and then visualize it on a graph.
Let's simplify the inequality step by step:
1. Distribute the -2 to the terms inside the parentheses:
3 - 2x - 8 ≤ 5
2. Combine like terms:
-2x - 5 ≤ 5
3. Add 5 to both sides of the inequality:
-2x ≤ 10
4. Divide both sides by -2, but remember to flip the inequality sign since we are dividing by a negative number:
x ≥ -5
Now that we have simplified the inequality, let's graph it on a number line:
-5------>
Since x is greater than or equal to -5, we will shade the number line to the right of -5.
So, the graph of the inequality 3−2(x+4)≤5 is a shaded region on the number line to the right of -5.
To match the inequality 3 − 2(x + 4) ≤ 5 to its graph, we need to simplify the expression first and solve for x.
Let's start by simplifying:
3 − 2(x + 4) ≤ 5
3 − 2x − 8 ≤ 5 (distribute the -2)
-2x - 5 ≤ 5 (combine like terms)
Next, we isolate the variable by adding 5 to both sides:
-2x - 5 + 5 ≤ 5 + 5
-2x ≤ 10
To solve for x, we divide both sides by -2, remembering that when dividing by a negative number, the inequality sign should be flipped:
(-2x)/(-2) ≥ 10/(-2)
x ≥ -5
Now that we have solved for x, we can graph the inequality on a number line. To do this:
1. Draw a number line.
2. Mark a point at -5, since x ≥ -5.
3. Draw a solid line pointing to the right from -5, indicating that all values greater than or equal to -5 satisfy the inequality.
The graph should look like this:
---------------------●>
...-8 -7 -6 -5 -4 -3 -2 -1 0 1 ...
The solid dot represents -5, and the arrow indicates all values greater than or equal to -5 satisfy the inequality.
Therefore, the matching graph for the inequality 3 − 2(x + 4) ≤ 5 is a number line with a solid dot at -5 and an arrow pointing to the right.