What is
5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13
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Answering yourself. How weird!
To solve the equation 5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13, we'll follow these steps:
Step 1: Simplify both sides of the equation.
Step 2: Combine like terms on both sides.
Step 3: Isolate the variable on one side of the equation.
Step 4: Solve for the variable.
Step 5: Verify the solution.
Let's go through each step in solving the equation:
Step 1: Simplify both sides of the equation.
On the left side, distribute the 5 to the terms inside the parentheses:
5 * -3x = -15x
5 * -2 = -10
So the left side becomes:
-15x - 10 - (x - 3)
On the right side, distribute the -4 to the terms inside the parentheses:
-4 * 4x = -16x
-4 * 5 = -20
So the right side becomes:
-16x - 20 + 13
Now the equation becomes:
-15x - 10 - (x - 3) = -16x - 20 + 13
Step 2: Combine like terms on both sides.
On the left side, combine the -10 and -3:
-10 - 3 = -13
So the left side becomes:
-15x - 13
On the right side, combine the -20 and 13:
-20 + 13 = -7
So the right side becomes:
-16x - 7
Now the equation becomes:
-15x - 13 = -16x - 7
Step 3: Isolate the variable on one side of the equation.
To do this, we'll move the terms with x to one side and the constant terms to the other side.
Let's start by moving the -16x term to the left side by adding 16x to both sides:
-15x - 13 + 16x = -16x - 7 + 16x
Simplifying both sides, we get:
x - 13 = -7
Next, let's move the constant term -13 to the right side by adding 13 to both sides:
x - 13 + 13 = -7 + 13
Simplifying both sides, we get:
x = 6
Step 4: Solve for the variable.
The solution to the equation is x = 6.
Step 5: Verify the solution.
To verify the solution, substitute x = 6 back into the original equation and see if both sides are equal.
Original equation:
5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
Substituting x = 6:
5(-3(6) - 2) - (6 - 3) = -4(4(6) + 5) + 13
Simplifying both sides, we get:
-75 = -75
Since both sides of the equation are equal, we can conclude that the solution x = 6 is correct.
Multiply factors.
-15x - 10 - x + 3 = -16x - 20 +13
Group like terms.
-16x - 7 = -16x - 7
Add 16x + 7 to both sides and write the equation as follows
0 = 0
The above statement is true for all values of x and therefore all real numbers are solutions to the given equation.