Questions: When solving linear equations with one variable, you must isolate the variable on one side of the equation. A mathematical property must validate each step taken in solving an equation. This ensures that equality is maintained throughout a solution. Some properties that you can use - addition property of equality - subtraction property of equality - multiplication property of equality - division property of equality - distributive property of multiplication over addition Explain each step in the solution to the equation 1/3(12x-9)=5x-7.

Solution Steps

The equation is given as: \[ \frac{1}{3}(12x - 9) = 5x - 7 \] To simplify the left side, we apply the distributive property of multiplication over addition. This means multiplying \(\frac{1}{3}\) by each term inside the parentheses: \[ \frac{1}{3} \cdot 12x - \frac{1}{3} \cdot 9 = 5x - 7 \] Simplifying this gives: \[ 4x - 3 = 5x - 7 \]

To isolate the variable \(x\), we use the subtraction property of equality. Subtract \(4x\) from both sides of the equation: \[ 4x - 3 - 4x = 5x - 7 - 4x \] Simplifying this gives: \[ -3 = x - 7 \]

Next, we use the addition property of equality to further isolate \(x\). Add \(7\) to both sides of the equation: \[ -3 + 7 = x - 7 + 7 \] Simplifying this gives: \[ 4 = x \]

Final Answer