Fill in the blanks to follow the steps in solving the equation:
5x − 12 − 6x = −10x + 7 − 1
Step 1: Combine like terms Response area
Step 2: Get the x-terms on the same side of the equation Response area
Step 3: Get the constants on the same side of the equation Response area
Step 4: Get the x by itself by using the inverse operation Response area
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Step 1: Combine like terms
5x - 12 - 6x = -10x + 7 - 1
(-12) - (-1) = (-10x) - (5x) + 7
-11 = -15x + 7
Step 2: Get the x-terms on the same side of the equation
-11 + 15x = -15x + 7
Step 3: Get the constants on the same side of the equation
-11 + 11 + 15x = -15x + 7 + 11
15x = -15x + 18
Step 4: Get the x by itself by using the inverse operation
15x + 15x = -15x + 15x + 18
30x = 18
Therefore, x = 18/30 which simplifies to x = 3/5
Step 1: Combine like terms
To combine like terms, we will start by adding or subtracting the x terms (coefficient times x) on both sides of the equation separately. On the left side, we have 5x and -6x, which combine to give -1x (or simply -x). On the right side, we have -10x, so we don't have any other x terms to combine. Now our equation looks like this:
-1x - 12 = -10x + 7 - 1
Step 2: Get the x-terms on the same side of the equation
In this step, we need to move all x-terms to one side of the equation. To do that, we can add 10x to both sides of the equation. By doing so, the x-terms on the right side will become 0x (which can be simply dropped since any number times 0 is 0). The equation now becomes:
-1x + 10x - 12 = 7 - 1
Step 3: Get the constants on the same side of the equation
Similarly, we need to move all the constants (numbers without x) to one side of the equation. To do that, we can add 12 to both sides of the equation. This will eliminate the constant term on the left side and give us:
10x = 7 - 1 + 12
Step 4: Get the x by itself by using the inverse operation
To solve for x, we want to get rid of the coefficient of 10 in front of x. The inverse operation of multiplying by 10 is dividing by 10. So, we will divide both sides of the equation by 10:
10x/10 = (7 - 1 + 12) / 10
This simplifies to:
x = (7 + 11) / 10
Thus, the solution to the equation is:
x = 18/10 or x = 9/5
Step 1: 11x - 12 = -10x + 7 - 1
Step 2: 11x - 10x = 7 - 1 - 12
Step 3: x = -4 - 12
Step 4: x = -16