Question: What is the solution set for this inequality?
8x + 2 < 10x - 4
a.) x < 3
b.) x < - 1
c.) x > 3
d.) x > - 1
1. **State the problem:** Solve the inequality $$8x + 2 < 10x - 4$$.
2. **Isolate variable terms:** Subtract $$8x$$ from both sides:
$$8x + 2 - 8x < 10x - 4 - 8x$$
which simplifies to
$$2 < 2x - 4$$
3. **Isolate constant terms:** Add $$4$$ to both sides:
$$2 + 4 < 2x - 4 + 4$$
which simplifies to
$$6 < 2x$$
4. **Solve for $$x$$:** Divide both sides by $$2$$:
$$\frac{6}{2} < \frac{2x}{2}$$
Show cancellation:
$$\frac{\cancel{6}}{\cancel{2}} < \frac{2x}{2}$$
which simplifies to
$$3 < x$$
or equivalently
$$x > 3$$
5. **Interpret the solution:** The solution set is all $$x$$ such that $$x > 3$$.
6. **Match with choices:** The correct answer is c.) $$x > 3$$.