Solving Linear Equations Using Properties of Equality

Q1. Solve the equation and check: $50x + 21 = 7(7x + 9)$

Background

Topic: Linear Equations and Properties of Equality

This question tests your ability to solve a linear equation by applying the distributive property, combining like terms, and isolating the variable using properties of equality.

Key Terms and Formulas:

• Distributive Property: $a(b + c) = ab + ac$

• Addition Property of Equality: If $a = b$, then $a + c = b + c$

• Combining Like Terms: Grouping terms with the same variable or constant

Step-by-Step Guidance

1. Apply the distributive property to remove parentheses on the right side: $7(7x + 9)$ becomes $49x + 63$.

2. Rewrite the equation: $50x + 21 = 49x + 63$.

3. Use the addition property of equality to isolate the variable. Subtract $49x$ from both sides: $50x + 21 - 49x = 49x + 63 - 49x$.

4. Combine like terms to simplify: $x + 21 = 63$.

Try solving on your own before revealing the answer!

Final Answer: $x = 42$

Subtract $21$from both sides to isolate$x$:$x = 63 - 21 = 42$.

To check, substitute $x = 42$ back into the original equation and verify both sides are equal.