7x + 12 = 3(5x - 12)
Step 1: Distribute the 3 to the numbers in the parentheses (5x and -12)
7x + 12 = (3 × 5x) + (3 × (-12))
7x + 12 = 15x + (-36)
Step 2: Combine like terms
x's go with x's (7x and 15x)
Subtract 7x to both sides
(7x - 7x) + 12 = (15x - 7x) + (-36)
(0) + 12 = 8x - 36
12 = 8x - 36
Normal numbers go with normal numbers
Add 36 to both sides
12 + 36 = 8x + (-36 + 36)
48 = 8x
Step 3: Isolate x by dividing 8 to both sides
48/8 = 8x/8
6 = x
Hope this helped!
Answer:
x = 6
Step-by-step explanation:
Eliminate parentheses using the distributive property.
7x +12 = 15x -36
You have x-terms and constants on both sides of the equal sign. One way to approach this is to find the x-term with the least coefficient (it is 7x) and subtract everything on that side of the equation.
(7x +12) -(7x +12) = (15x -36) -(7x +12)
Simplify, also known as "collect terms."
0 = 8x -48
Now, divide by the coefficient of x: 8.
0 = x -6
Add the opposite of the constant: 6.
6 = x
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Alternate solution
By looking for the x-term with the smallest coefficient, we get a positive result when we subtract that term. If we were to subtract 15x from both sides of the equation, it would be ...
-8x +12 = -36 . . . . . . . with a negative x-coefficient
You can still work the problem this way, but it can introduce errors if you're not careful with signs. To finish this, we would subtract 12 to get the x-term by itself:
-8x = -48
Then we would divide by the x-coefficient, -8.
x = -48/-8 = 6 . . . . . same solution; same number of steps
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Whenever you add, subtract, multiply, divide, you do the same thing to both sides of the equation.
