Solve the following linear inequalities using the addition and subtraction properties of equality.

• A. $x<2$
• B. $x>2$
• C. $x<1.8$
• D. $x\le1.8$

Answer: (A)

Verified step by step guidance

1. Start with the given inequality: \$7x + 3 < 2x + 13$.
2. Use the subtraction property of inequality to get all terms involving \(x\) on one side. Subtract \$2x\( from both sides: \)7x - 2x + 3 < 2x - 2x + 13\(, which simplifies to \)5x + 3 < 13$.
3. Next, isolate the term with \(x\) by subtracting 3 from both sides: \$5x + 3 - 3 < 13 - 3\(, which simplifies to \)5x < 10$.
4. Now, solve for \(x\) by dividing both sides by 5 (note that since 5 is positive, the inequality direction remains the same): \(\frac{5x}{5} < \frac{10}{5}\), which simplifies to \(x < 2\).
5. The solution to the inequality is \(x < 2\), meaning all values of \(x\) less than 2 satisfy the original inequality.