Question

Can you find x for the following equation?
7x+12=3(5x-12)

Answer 1

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 2

x = 6

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.