Fill in the blanks to explain what needs to be done in the current step to get to the next step.
3x+4−2x+9=17−x
Step 1: 3x+4−2x+9=17−x
Step 2: x+13= 17−x
Step 3: x+x+13=17−x+x
Step 4: 2x +13 = 17
Step 5: 2x+13−13=17−13
Step 6: 2x=4
Step 7: x = 2
ANSWER CHOICES: Distributive Property, Addition/ Subtraction Property of Equality, Multiplication/ Division Property of equality, Combine like terms
Step 1: Distributive Property
Step 2: Addition/ Subtraction Property of Equality
Step 3: Combine like terms
Step 4: Addition/ Subtraction Property of Equality
Step 5: Addition/ Subtraction Property of Equality
Step 6: Multiplication/ Division Property of Equality
Step 7: Multiplication/ Division Property of Equality
Step 1: 3x+4−2x+9=17−x
Step 2: x+13= 17−x
Explanation: Combine like terms on the left side by combining 3x and -2x.
Step 3: x+x+13=17−x+x
Explanation: Combine like terms on the left side by combining x and -x.
Step 4: 2x +13 = 17
Explanation: Simplify the left side of the equation.
Step 5: 2x+13−13=17−13
Explanation: Subtract 13 from both sides of the equation.
Step 6: 2x=4
Explanation: Simplify both sides of the equation.
Step 7: x = 2
Explanation: Divide both sides of the equation by 2.
Answer: Multiplication/ Division Property of equality
Step 1: The equation 3x+4−2x+9=17−x is given.
Step 2: To simplify the equation, we need to combine like terms. In this case, we can combine the x terms on both sides of the equation. Subtracting x from both sides, we get x+13= 17−x.
Step 3: Next, we can combine the x terms by adding x to both sides of the equation. This gives us x+x+13=17−x+x.
Step 4: By combining like terms on the left side, we get 2x +13 = 17.
Step 5: To simplify further, we can subtract 13 from both sides of the equation. Thus, we have 2x+13−13=17−13.
Step 6: After subtracting, we end up with 2x=4.
Step 7: Finally, to isolate x, we can divide both sides of the equation by 2. Consequently, x = 2.
To solve this equation, we used the following properties:
- Step 2, 4, and 7: We used the Addition/Subtraction Property of Equality, which allows us to add or subtract the same value from both sides of the equation.
- Step 3: We applied the Distributive Property to simplify the expression.
- Step 6: We used the Multiplication/Division Property of Equality, which allows us to multiply or divide both sides of the equation by the same value.
- Step 4 and 5: We combined like terms using the Commutative and Associative Properties of Addition.