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

• A.
• B. $x>2$
• C.
• D. $x\le 1.8$

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 the \(x\) terms on one side. Subtract \$2x$ from both sides: \(7x - 2x + 3 < 2x - 2x + 13\), which simplifies to \(5x + 3 < 13\).
3. Next, use the subtraction property again to isolate the term with \(x\). Subtract \(3\) from both sides: \(5x + 3 - 3 < 13 - 3\), which simplifies to \(5x < 10\).
4. Now, use the division property of inequality to solve for \(x\). Divide both sides by \(5\): \(\frac{5x}{5} < \frac{10}{5}\), 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.