Drag each tile to the correct location on the table. Each tile can be used more than once, but not all tiles will be used. Choose the justification for each step in the solution to the given equation.
Simplification
subtraction property of equality
addition property of equality
division property of equality
multiplication property of equality
| Step | Justification |
| --- | --- |
| [tex]\frac{17}{3}-\frac{3}{4} x=\frac{1}{2} x+5[/tex] | given |
| [tex]\frac{17}{3}-\frac{3}{4} x-\frac{17}{3}=\frac{1}{2} x+5-\frac{17}{3}[/tex] | |
| [tex]-\frac{3}{4} x=\frac{1}{2} x-\frac{2}{3}[/tex] | |
| [tex]-\frac{3}{4} x-\frac{1}{2} x=\frac{1}{2} x-\frac{2}{3}-\frac{1}{2} x[/tex] | |
| [tex]-\frac{5}{4} x=-\frac{2}{3}[/tex] | |
| [tex]-\frac{5}{4} x \cdot-\frac{4}{5}=-\frac{2}{3} \cdot-\frac{4}{5}[/tex] | |
| [tex]x=\frac{8}{15}[/tex] | |
Answer (1)
Step 1: Apply the subtraction property of equality.
Step 2: Simplify the equation.
Step 3: Apply the subtraction property of equality again.
Step 4: Simplify the equation further and apply the multiplication property of equality.
Step 5: Simplify to find the final answer: x = 15 8 .
Explanation
Understanding the Problem We are given an equation and a step-by-step solution. Our task is to provide the justification for each step in the solution. The available justifications are: Simplification, Subtraction Property of Equality, Addition Property of Equality, Division Property of Equality, and Multiplication Property of Equality.
Step 1: Given Step 1: 3 17 − 4 3 x = 2 1 x + 5 is given.
Step 2: Subtraction Property of Equality Step 2: 3 17 − 4 3 x − 3 17 = 2 1 x + 5 − 3 17 . We subtracted 3 17 from both sides of the equation. This is justified by the Subtraction Property of Equality.
Step 3: Simplification Step 3: − 4 3 x = 2 1 x − 3 2 . On the left side, 3 17 − 4 3 x − 3 17 simplifies to − 4 3 x . On the right side, 5 − 3 17 = 3 15 − 3 17 = − 3 2 . Therefore, the justification is Simplification.
Step 4: Subtraction Property of Equality Step 4: − 4 3 x − 2 1 x = 2 1 x − 3 2 − 2 1 x . We subtracted 2 1 x from both sides of the equation. This is justified by the Subtraction Property of Equality.
Step 5: Simplification Step 5: − 4 5 x = − 3 2 . On the left side, − 4 3 x − 2 1 x = − 4 3 x − 4 2 x = − 4 5 x . Therefore, the justification is Simplification.
Step 6: Multiplication Property of Equality Step 6: − 4 5 x ⋅ − 5 4 = − 3 2 ⋅ − 5 4 . We multiplied both sides of the equation by − 5 4 . This is justified by the Multiplication Property of Equality.
Step 7: Simplification Step 7: x = 15 8 . On the left side, − 4 5 x ⋅ − 5 4 = x . On the right side, − 3 2 ⋅ − 5 4 = 15 8 . Therefore, the justification is Simplification.
Examples
When solving equations in physics or engineering, it's crucial to justify each step to ensure the correctness of the solution. For example, if you're analyzing a circuit and need to find the current, you might use algebraic manipulations to isolate the variable representing the current. Each step, like adding or multiplying by a constant, must be justified by the properties of equality to maintain the balance of the equation and arrive at the correct value for the current. This ensures the circuit analysis is accurate and reliable.
