Do I have this right? These were very confusing.
16 = 4(x – 8) Given
16 = 4x -32 Distributive Property
16 + 32 = 4x -32 + 32 Addition Property of Equality
48 = 4x + 0 Combine like terms?
48 = 4x Identity Prop of Addition
48/4 = 4x/4 Division Prop of Equal
12 = x1 Division?
12 = 1x Commutative Prop of Multip?
12 = xIdentity Prop of Mult?
maybe a couple of extra steps. but the properties are all correct.
Yes, you have the steps mostly correct. Let me explain each step in detail:
Step 1: Start with the equation 16 = 4(x - 8) - This is the given equation.
Step 2: Use the distributive property to remove the parentheses: 16 = 4x - 32.
Step 3: Add 32 to both sides of the equation to isolate the term with x on one side: 16 + 32 = 4x - 32 + 32. This is the addition property of equality.
Step 4: Simplify both sides of the equation: 48 = 4x + 0. The 32 and -32 terms cancel each other out, so we are left with 4x on the right side.
Step 5: You correctly identified that 0 added to any number gives the same number itself, so 4x + 0 simplifies to 4x.
Step 6: Divide both sides of the equation by 4 to solve for x: 48/4 = 4x/4. This is the division property of equality.
Step 7: Simplify both sides of the equation: 12 = x. Here, x/4 divided by 4 gives x/16.
So, the final solution is x = 12.
Yes, you have the explanation correct. Let me quickly go through each step to make sure we are on the same page.
Step 1: The given equation is 16 = 4(x - 8). This equation is asking you to solve for x.
Step 2: In order to solve the equation, you need to apply the Distributive Property. Distribute 4 to both terms inside the parentheses, giving you 16 = 4x - 32.
Step 3: To isolate the variable term, which is 4x, you want to move the constant term (-32) to the other side of the equation. To do this, use the Addition Property of Equality. Add 32 to both sides of the equation, resulting in 16 + 32 = 4x - 32 + 32.
Step 4: Simplify both sides of the equation. On the left side, 16 + 32 equals 48. On the right side, -32 + 32 cancels out, leaving you with 4x + 0, which simplifies to 4x.
Step 5: Now, you have the equation 48 = 4x.
Step 6: To solve for x, you need to use the Division Property of Equality. Divide both sides of the equation by 4, which gives you 48/4 = 4x/4.
Step 7: Simplify both sides of the equation. On the left side, 48 divided by 4 equals 12. On the right side, 4x divided by 4 simplifies to x.
Step 8: Now, you have the solution: x = 12.
In conclusion, you have successfully solved the equation 16 = 4(x - 8) and found the value of x, which is 12.