Answer
The solution is x = -57
Work Step by Step
Let's start with the equation, as it is written.
10(z + 4) - 4(z - 2) = 3(z - 1) + 2(z - 3)
We start by completing the distributive property with the numeric values in front of each set of parentheses. We need to simplify both sides of the equation in order to solve it.
10z + 40 - 4z + 8 = 3z - 3 + 2z - 6
Now that we have applied the distributive property, taking note of all signs, we can regroup the terms on each side of the equation so that like terms are grouped together.
10z - 4z + 40 + 8 = 3z + 2z - 3 - 6
We can now combine like terms on each side of the equation. Remember: like terms must have exactly the same variable parts.
6z + 48 = 5z - 9
Last, we want to get all the variable terms on one side of the equation and all of the constant terms on the other side of the equation. We can start by subtracting 5z from both sides of the equations.
6z - 5z + 48 = 5z - 5z - 9
Complete the arithmetic.
z + 48 = -9
Now, let's subtract 48 from both sides of the equation.
z + 48 - 48 = -9 - 48
Complete the arithmetic.
z = -57
Our answer can by checked by substituting it back into the original equation and then simplifying each side. If we get the same number on both sides of the equation, we have solved it correctly.
10(z + 4) - 4(z - 2) = 3(z - 1) + 2(z - 3)
Substituting x = -57, we get:
10(-57 + 4) - 4(-57 - 2) = 3(-57 - 1) + 2(-57 - 3)
Work within the parentheses:
10(-53) - 4(-59) = 3(-58) + 2(-60)
Then we can multiply on both sides of the equation.
-530 + 236 = -174 - 120
Now add/subtract on each side of the equation.
-294 = -294
Our values simplify to the same number, so our solution of x = -57 is correct.
