Solve the linear equation using any technique you have learned. Name the technique. Check.
3x + 12 = -7x - 28
I know the answer is x = -4
and I know that substitution is the technique that is used, but I can't figure out how to set this up
3(-4) + 12 = -7(-4) - 28
-12 + 12 = 28 - 28
0 = 0
3x + 12 = -7x - 28
Add 7x to both sides
3x + 12 + 7x = -7x - 28 + 7x
10x + 12 = -28
Now subtract 12 from both sides
10x + 12 - 12 = -28 - 12
10x = -40
now divide both terms by 10
x = -4
To solve the given linear equation, we can use the technique of simplifying and rearranging the equation. Here's how you can set it up using the substitution method:
Given equation: 3x + 12 = -7x - 28
Step 1: Start by isolating one variable on one side of the equation. Let's isolate the term with "x" on the left side. To do that, we need to shift the terms containing "x" from the right side to the left side.
Add 7x to both sides of the equation to eliminate the -7x term on the right side: 3x + 7x + 12 = -7x + 7x - 28
Simplifying the equation: 10x + 12 = -28
Step 2: Next, isolate the x-term by moving the constant term (in this case, 12) to the right side. Subtract 12 from both sides of the equation: 10x + 12 - 12 = -28 - 12
Simplifying the equation: 10x = -40
Step 3: Now, we want to solve for x. To do so, divide both sides of the equation by the coefficient of x, which is 10: (10x) / 10 = (-40) / 10
Simplifying the equation: x = -4
So, the solution to the given linear equation is x = -4.
To check if this is the correct solution, substitute x = -4 back into the original equation and see if both sides are equal:
Original equation: 3x + 12 = -7x - 28
Substituting x = -4: 3(-4) + 12 = -7(-4) - 28
Simplifying the equation: -12 + 12 = 28 - 28
The left side equals 0, and the right side also equals 0. Therefore, the solution x = -4 is verified.