4(k+1)–18.35>
–
5.19
Write your answer using a decimal, whole number, or fraction in lowest terms.



To solve the inequality:

\[
4(k+1) - 18.35 > -5.19
\]

### Step 1: Expand the left-hand side.

Distribute the 4 through the expression \( (k+1) \):

\[
4(k + 1) = 4k + 4
\]

Now substitute this back into the inequality:

\[
4k + 4 - 18.35 > -5.19
\]

### Step 2: Simplify the left-hand side.

Combine the constants \( 4 - 18.35 \):

\[
4k - 14.35 > -5.19
\]

### Step 3: Isolate \( 4k \).

Add 14.35 to both sides to move the constant to the right-hand side:

\[
4k > -5.19 + 14.35
\]

Simplify the right-hand side:

\[
4k > 9.16
\]

### Step 4: Solve for \( k \).

Divide both sides by 4:

\[
k > \frac{9.16}{4}
\]

Now simplify the fraction:

\[
k > 2.29
\]

### Final Answer:

The solution is \( k > 2.29 \).

Do you have any questions, or would you like more details?

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Here are five related questions:
1. How would the inequality change if the constant term was negative on both sides?
2. What happens if you multiply or divide an inequality by a negative number?
3. How do you solve an inequality involving fractions?
4. How do you check if a specific value satisfies the inequality?
5. Can this inequality have a solution in terms of an interval?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the linear inequality 4(k+1) - 18.35 > -5.19 with a step-by-step guide. This problem involves expanding, simplifying, and isolating variables, providing a clear explanation of key algebraic concepts. Suitable for students in Grades 8-10.

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