Simplifying with addition and subtraction
We can use addition and subtraction to get all the terms with variables on one side of an equation, and all the numeric terms on the other.
The equations 3x = 17, 21 = y, and z/12 = 24 each have a variable term on one side of the = sign, and a number on the other.
The equations x + 3 = 12, 21 = 30 - y, and (z + 2) × 4 = 10 do not.
We usually do this after simplifying each side using the distributive rules, eliminating parentheses, and combining like terms. Since addition is associative, it can be helpful to add a negative number to each side instead of subtracting to avoid mistakes.
Examples:
For the equation 3x + 4 = 12, we can isolate the variable term on the left by subtracting a 4 from both sides:
3x + 4 - 4 = 12 - 4 ==>
3x = 8.
For the equation 7y - 200 = 10, subtracting the 200 on the left side is the same as adding a -200:
7y + (-200) = 10.
If we add 200 to both sides of the equation, the 200 and -200 will cancel each other:
7y + (-200) + 200 = 10 + 200 ==>
7y = 210.
For the equation 8 = 20 - z, we can add z to both sides to get 8 + z = 20 - z + z ==> 8 + z = 20. Now subtracting 8 from both sides,
8 + z - 8 = 20 - 8 ==>
z = 12, so we get a solution for z.
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