Let's solve
Problem #10 from the image, which is:
> Solve the inequality:
> $$
> 5x - (9x + 14) < 3(x + 10) - 2
> $$
We'll go step by step.
---
Step 1: Simplify both sides of the inequality
Start by distributing and simplifying each side.
#### Left Side:
$$
5x - (9x + 14)
$$
Distribute the negative sign:
$$
5x - 9x - 14 = -4x - 14
$$
#### Right Side:
$$
3(x + 10) - 2
$$
Distribute the 3:
$$
3x + 30 - 2 = 3x + 28
$$
Now the inequality becomes:
$$
-4x - 14 < 3x + 28
$$
---
Step 2: Move all variable terms to one side
Subtract $3x$ from both sides:
$$
-4x - 3x - 14 < 28
\Rightarrow -7x - 14 < 28
$$
---
Step 3: Move constant terms to the other side
Add 14 to both sides:
$$
-7x < 28 + 14
\Rightarrow -7x < 42
$$
---
Step 4: Solve for $x$
Divide both sides by $-7$.
⚠️
Remember: When dividing or multiplying both sides of an inequality by a
negative number, you must
reverse the inequality sign.
$$
x > \frac{42}{-7}
\Rightarrow x > -6
$$
---
✔ Final Answer:
$$
\boxed{x > -6}
$$
Which corresponds to choice
C) $x > -6$
---
📌 Answer: C) $x > -6$
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Let me know if you'd like help with any of the other problems (like #1 or #6)!
Parent Tip: Review the logic above to help your child master the concept of solving multi step inequalities worksheet answers.
