Choose the correct solution and graph for the inequality. z - 6 < - 14
The correct solution for the inequality is z < -8, and the graph of the solution is an open circle at -8 on the number line, shaded to the left.
To solve the inequality z - 6 < -14, you can follow these steps:
Step 1: Add 6 to both sides of the inequality to isolate the variable z:
z - 6 + 6 < -14 + 6
z < -8
Step 2: Graph the solution on a number line. Draw an open circle on -8 and shade the line to the left, indicating that z is less than -8.
So, the correct solution is z < -8, and the graph would be represented as:
----<=======o
Choose the correct solution and graph for the inequality.
y - 1/3 > 1/8
(1 point)
To solve the inequality y - 1/3 > 1/8, you can follow these steps:
Step 1: Add 1/3 to both sides of the inequality to isolate the variable y:
y - 1/3 + 1/3 > 1/8 + 1/3
y > 1/8 + 1/3
Step 2: Add the fractions 1/8 and 1/3:
1/8 + 1/3 = 3/24 + 8/24 = 11/24
So the inequality becomes:
y > 11/24
Step 3: Graph the solution on a number line. Draw an open circle on 11/24 and shade the line to the right, indicating that y is greater than 11/24.
The correct solution is y > 11/24, and the graph would be represented as:
-------o========>
To solve the inequality z - 6 < -14, we need to isolate the variable z.
Here are the steps to solve the inequality:
1. Add 6 to both sides of the inequality:
z - 6 + 6 < -14 + 6
Simplifying:
z < -8
Now, let's graph the solution on the number line:
1. Draw a number line with a point at -8 (since z < -8).
2. Since the inequality is not inclusive, we will leave an open circle at -8.
3. Shade the portion of the number line to the left of -8, indicating that z can be any value less than -8.
The graph should represent all values of z that are less than -8 on the number line.
q + 1/3 > 1/2 (1 point)
Choose the correct solution and graph for the inequality.
To solve the inequality q + 1/3 > 1/2, you can follow these steps:
Step 1: Subtract 1/3 from both sides of the inequality to isolate the variable q:
q + 1/3 - 1/3 > 1/2 - 1/3
q > 1/2 - 1/3
Step 2: Subtract the fractions 1/2 and 1/3:
1/2 - 1/3 = 3/6 - 2/6 = 1/6
So the inequality becomes:
q > 1/6
Step 3: Graph the solution on a number line. Draw an open circle on 1/6 and shade the line to the right, indicating that q is greater than 1/6.
The correct solution is q > 1/6, and the graph would be represented as:
--------o======>
Choose the correct solution and graph for the inequality.
z + 9 <= 6 (1 point)
To solve the inequality z + 9 <= 6, you can follow these steps:
Step 1: Subtract 9 from both sides of the inequality to isolate the variable z:
z + 9 - 9 <= 6 - 9
z <= -3
Step 2: Graph the solution on a number line. Draw a closed circle on -3 and shade the line to the left, indicating that z is less than or equal to -3.
The correct solution is z <= -3, and the graph would be represented as:
o======<
Choose the correct solution and graph for the inequality.
y/3 >= - 5
(1point)