Question

Solve for f.
f/–1–65≤–71

Answer 1

Solve for t.
–89<t–30–90

Answer 2

Solve for p.
–64–33p≤–31

Answer 3

Solve for a.
47>a/7+41

Answer 4

Solve for b.
13b+8≤–5

Answer 5

Solve for t.
–79≤t20–84

Answer 6

To solve the inequality \( \frac{f}{-1} - 65 \leq -71 \), we will follow these steps:

1. **Isolate the fraction**:
\[
\frac{f}{-1} - 65 \leq -71
\]
Add 65 to both sides:
\[
\frac{f}{-1} \leq -71 + 65
\]
Simplifying the right-hand side gives:
\[
\frac{f}{-1} \leq -6
\]

2. **Multiply both sides by -1**:
Please remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality. Hence,
\[
f \geq 6
\]

Thus, the solution is:
\[
f \geq 6
\]

Answer 7

To solve the inequality \( -89 < t - 30 - 90 \), we will first simplify the right side of the inequality:

1. **Combine like terms**:
\[
-89 < t - 30 - 90
\]
Simplifying the right side:
\[
-89 < t - 120
\]

2. **Isolate \( t \)**:
Add 120 to both sides:
\[
-89 + 120 < t
\]
This simplifies to:
\[
31 < t
\]

3. **Rewrite the inequality**:
The above can be rewritten in standard form:
\[
t > 31
\]

Thus, the solution is:
\[
t > 31
\]

Answer 8

To solve the inequality \( -64 - 33p \leq -31 \), we'll follow these steps:

1. **Isolate the term with \( p \)**:
Start by adding 64 to both sides of the inequality:
\[
-64 - 33p + 64 \leq -31 + 64
\]
This simplifies to:
\[
-33p \leq 33
\]

2. **Divide by -33**:
When dividing both sides of an inequality by a negative number, remember to reverse the inequality sign:
\[
p \geq \frac{33}{-33}
\]
Simplifying gives:
\[
p \geq -1
\]

Thus, the solution is:
\[
p \geq -1
\]

Answer 9

To solve the inequality \( 47 > \frac{a}{7} + 41 \), follow these steps:

1. **Isolate the term with \( a \)**:
Start by subtracting 41 from both sides:
\[
47 - 41 > \frac{a}{7}
\]
This simplifies to:
\[
6 > \frac{a}{7}
\]

2. **Multiply both sides by 7**:
Since 7 is positive, the direction of the inequality remains the same:
\[
6 \cdot 7 > a
\]
This simplifies to:
\[
42 > a
\]
or, equivalently,
\[
a < 42
\]

Thus, the solution is:
\[
a < 42
\]

Answer 10

To solve the inequality \( 13b + 8 \leq -5 \), follow these steps:

1. **Isolate the term with \( b \)**:
Start by subtracting 8 from both sides:
\[
13b + 8 - 8 \leq -5 - 8
\]
This simplifies to:
\[
13b \leq -13
\]

2. **Divide by 13**:
Now, divide both sides by 13. Since 13 is positive, the inequality direction remains the same:
\[
b \leq \frac{-13}{13}
\]
This simplifies to:
\[
b \leq -1
\]

Thus, the solution is:
\[
b \leq -1
\]

Answer 11

To solve the inequality \(-79 \leq t \cdot 20 - 84\), follow these steps:

1. **Isolate the term with \( t \)**:
Start by adding 84 to both sides:
\[
-79 + 84 \leq t \cdot 20
\]
This simplifies to:
\[
5 \leq t \cdot 20
\]

2. **Divide by 20**:
Now, divide both sides by 20 (since 20 is positive, the direction of the inequality remains the same):
\[
\frac{5}{20} \leq t
\]
Simplifying gives:
\[
\frac{1}{4} \leq t
\]
or equivalently,
\[
t \geq \frac{1}{4}
\]

Thus, the solution is:
\[
t \geq \frac{1}{4}
\]