j - (5 - 3j) = 7j + 4
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j - (5 - 3j) = 7j + 4
First, distribute the negative sign:
j - 5 + 3j = 7j + 4
Combine like terms:
4j - 5 = 7j + 4
Subtract 4j from both sides:
-5 = 3j + 4
Subtract 4 from both sides:
-9 = 3j
Divide both sides by 3:
-3 = j
Therefore, the solution is j = -3.
-6/5(4x - 3) = -6/3(4x - 4)
show all work
To solve this equation, we will first distribute the terms on each side.
-6/5(4x - 3) = -6/3(4x - 4)
Let's start by simplifying both sides.
On the left side:
-6/5 * 4x = -24x/5
-6/5 * -3 = 18/5
So, the left side of the equation becomes:
-24x/5 + 18/5
On the right side:
-6/3 * 4x = -24x/3
-6/3 * -4 = 24/3 = 8
So, the right side of the equation becomes:
-24x/3 + 8
Now, the equation becomes:
-24x/5 + 18/5 = -24x/3 + 8
To eliminate the denominators, we can multiply both sides of the equation by the least common denominator (LCD), which is 15.
15 * (-24x/5 + 18/5) = 15 * (-24x/3 + 8)
Expanding both sides:
-72x + 54 = -120x + 120
Next, we simplify the equation:
-72x + 54 = -120x + 120
To get rid of the x term on the right side, we will add 120x to both sides:
-72x + 120x + 54 = -120x + 120x + 120
This simplifies to:
48x + 54 = 120
Next, we subtract 54 from both sides:
48x + 54 - 54 = 120 - 54
This simplifies to:
48x = 66
Finally, we divide both sides by 48 to solve for x:
x = 66/48
Which simplifies to:
x = 11/8
find any mistakes:
Given: 3(r - 2) = r + 6
Step 1: 3r - 2 = r + 6
Step 2: 2r - 2 = 6
Step 3: 2r = 8
Step 4: r = 4
There are no mistakes in the solution. Well done!
are you sure
My apologies for the confusion. You are correct, there is a mistake in the solution.
Given: 3(r - 2) = r + 6
Step 1: Distribute the 3 on the left side: 3r - 6 = r + 6
Step 2: Subtract r from both sides: 2r - 6 = 6
Step 3: Add 6 to both sides: 2r = 12
Step 4: Divide both sides by 2: r = 6
So the correct solution is r = 6. Thank you for pointing out the error.