Question

Solve for d.
15<6d–3

Answer 1

Solve for d.
3 - –1d≤1

Answer 2

Solve for y.
1≥y/7–1

Answer 3

Solve for p.
p/2–1<4

Answer 4

Solve for g.
4g+20>4

Answer 5

Solve for r.
2r+1≥9

Answer 6

To solve the inequality \( 15 < 6d - 3 \), follow these steps:

1. **Add 3 to both sides**:
\[
15 + 3 < 6d
\]
\[
18 < 6d
\]

2. **Divide by 6**:
\[
\frac{18}{6} < d
\]
\[
3 < d
\]

This can also be written as:
\[
d > 3
\]

So, the solution is \( d > 3 \).

Answer 7

To solve the inequality \( 3 - (-1d) \leq 1 \), we first rewrite it:

1. Rewrite the negative sign:
\[
3 + d \leq 1
\]

2. Subtract 3 from both sides:
\[
d \leq 1 - 3
\]
\[
d \leq -2
\]

So the solution is \( d \leq -2 \).

Answer 8

To solve the inequality \(1 \geq \frac{y}{7} - 1\), follow these steps:

1. **Add 1 to both sides**:
\[
1 + 1 \geq \frac{y}{7}
\]
\[
2 \geq \frac{y}{7}
\]

2. **Multiply both sides by 7** (since 7 is positive, the direction of the inequality does not change):
\[
2 \cdot 7 \geq y
\]
\[
14 \geq y
\]

This can also be written as:
\[
y \leq 14
\]

So, the solution is \(y \leq 14\).

Answer 9

To solve the inequality \( \frac{p}{2} - 1 < 4 \), follow these steps:

1. **Add 1 to both sides**:
\[
\frac{p}{2} < 4 + 1
\]
\[
\frac{p}{2} < 5
\]

2. **Multiply both sides by 2** (since 2 is positive, the direction of the inequality does not change):
\[
p < 5 \cdot 2
\]
\[
p < 10
\]

So, the solution is \( p < 10 \).

Answer 10

To solve the inequality \( 4g + 20 > 4 \), follow these steps:

1. **Subtract 20 from both sides**:
\[
4g + 20 - 20 > 4 - 20
\]
\[
4g > -16
\]

2. **Divide both sides by 4**:
\[
g > \frac{-16}{4}
\]
\[
g > -4
\]

So, the solution is \( g > -4 \).

Answer 11

To solve the inequality \( 2r + 1 \geq 9 \), follow these steps:

1. **Subtract 1 from both sides**:
\[
2r + 1 - 1 \geq 9 - 1
\]
\[
2r \geq 8
\]

2. **Divide both sides by 2**:
\[
r \geq \frac{8}{2}
\]
\[
r \geq 4
\]

So, the solution is \( r \geq 4 \).