Question

Solve the inequality.
1. -(7c -18) -2c > 0
2. 4v + 8 greater than or equal to 6v + 10

Answer 1

Let's solve each inequality step by step.

### 1. Solve the inequality \( -(7c - 18) - 2c > 0 \)

Start by distributing the negative sign:

\[
-7c + 18 - 2c > 0
\]

Combine like terms:

\[
-7c - 2c + 18 > 0
\]
\[
-9c + 18 > 0
\]

Next, subtract 18 from both sides:

\[
-9c > -18
\]

Now, divide both sides by -9. Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign:

\[
c < 2
\]

So the solution for the first inequality is:

\[
c < 2
\]

### 2. Solve the inequality \( 4v + 8 \geq 6v + 10 \)

Start by moving all terms involving \(v\) to one side and constant terms to the other side:

\[
4v + 8 - 6v \geq 10
\]
\[
-2v + 8 \geq 10
\]

Next, subtract 8 from both sides:

\[
-2v \geq 2
\]

Now, divide both sides by -2, reversing the inequality sign:

\[
v \leq -1
\]

So the solution for the second inequality is:

\[
v \leq -1
\]

### Summary of Solutions:

1. \( c < 2 \)
2. \( v \leq -1 \)