Drag and drop the correct justifications into the boxes.
4(x−2)+1=9 : subtraction property of equality
4x−8+1=9 :combine like terms
4x−7=9 : distributive property
4x = 16 : associative property of equality
x = 4 : division property of equality
4(x−2)+1=9 --> 4x−8+1=9
you used the distributive property
4x−8+1=9 --> 4x - 7 = 9
you simplified or added like terms
4x - 7 = 9 --> 4x = 16
you added 7 to both sides, rules of equation
4x = 16 ----> x = 4
you divided both sides by 4, rules of equation
I don't know what "justifications" were available for you
To solve the equation 4(x−2)+1=9, you want to simplify the expression on the left side of the equation until you isolate the variable x. Here's how you can do it:
Step 1: Apply the subtraction property of equality by subtracting 1 from both sides:
4(x−2)+1 - 1 = 9 - 1
which simplifies to:
4(x−2) = 8
Step 2: Use the distributive property to multiply 4 by each term inside the parentheses:
4 * x - 4 * 2 = 8
which simplifies to:
4x - 8 = 8
Step 3: Combine like terms by adding 8 to both sides:
4x - 8 + 8 = 8 + 8
which simplifies to:
4x = 16
Step 4: Apply the associative property of equality by dividing both sides by 4:
(4x)/4 = 16/4
which simplifies to:
x = 4
Therefore, the correct justifications for each step are:
Step 1: subtraction property of equality
Step 2: distributive property
Step 3: combine like terms
Step 4: division property of equality