Question

Use the properties of inequality to find the solution to 5(2k-3)>-(4-3k)

Answer 1

To solve the inequality \( 5(2k - 3) > - (4 - 3k) \), we can first simplify both sides of the inequality step by step.

1. **Distribute on the left side**:
\[
5(2k - 3) = 10k - 15
\]

2. **Distribute the negative sign on the right side**:
\[
- (4 - 3k) = -4 + 3k
\]

So, the inequality now reads:
\[
10k - 15 > -4 + 3k
\]

3. **Rearrange the inequality** by getting all terms involving \( k \) on one side and constant terms on the other side. Subtract \( 3k \) from both sides:
\[
10k - 3k - 15 > -4
\]
Simplifying that gives:
\[
7k - 15 > -4
\]

4. **Add 15 to both sides**:
\[
7k > -4 + 15
\]
Simplifying that results in:
\[
7k > 11
\]

5. **Divide both sides by 7**:
\[
k > \frac{11}{7}
\]

So, the solution to the inequality \( 5(2k - 3) > - (4 - 3k) \) is:
\[
k > \frac{11}{7}
\]