3(w-6)-2(4-w) = 0
solution: 3w-18-8+2w = 0
5w-26 = 0
5w = 26
w = 26/5
solution: 3w-18-8+2w = 0
5w-26 = 0
5w = 26
w = 26/5
How Do I Solve 3(w-6)-2(4-w)=0 If The Answer Is 26/5?
Given
3(w-6) - 2(4-w) = 0
Solution
3w -3(6) - 2(4) -2(-w) = 0 (distributive property)
3w+2w -18 -8 = 0 (associative property)
5w - 26 = 0 (associative property)
5w = 26 (add 26 to both sides)
w = 26/5 (divide both sides by 5)
Check
3(26/5-6) - 2(4-26/5) = 0
3(26/5-30/5) - 2(20/5-26/5) = 0
3(-4/5) - 2(-6/5) = 0
-12/5 + 12/5 = 0
0 = 0 (check!)
Generally, the idea is to isolate the variable of interest on one side of the equation by "undoing" whatever was done to it. Here we simplify the expression so we can get all of the variable terms together (5w) and all of the constant terms together (-26). Then we set about getting to the variable itself, first by getting only the variable term on one side of the equal sign. Then we divide by what it had been multiplied by, so as to get just one times the variable.
The above is the approach for linear equations (no variables multiplied by themselves or any other variables). For quadratic equations, the approach is similar, but different, often to put the equation in "standard form" and solve it using a formula for the solution.
One key to algebra is to keep the equal sign sacred. Never violate it. Make sure it is always true that what is on one side is equal to what is on the other side. (It may look like things are being moved from one side to the other, and they are. But note that we do it by performing the same operation on both sides of the equal sign, so the two sides of the equation remain equal.)
It is always a good idea to check your work, preferably in such a way that you don't make the same mistake twice.
3(w-6) - 2(4-w) = 0
Solution
3w -3(6) - 2(4) -2(-w) = 0 (distributive property)
3w+2w -18 -8 = 0 (associative property)
5w - 26 = 0 (associative property)
5w = 26 (add 26 to both sides)
w = 26/5 (divide both sides by 5)
Check
3(26/5-6) - 2(4-26/5) = 0
3(26/5-30/5) - 2(20/5-26/5) = 0
3(-4/5) - 2(-6/5) = 0
-12/5 + 12/5 = 0
0 = 0 (check!)
Generally, the idea is to isolate the variable of interest on one side of the equation by "undoing" whatever was done to it. Here we simplify the expression so we can get all of the variable terms together (5w) and all of the constant terms together (-26). Then we set about getting to the variable itself, first by getting only the variable term on one side of the equal sign. Then we divide by what it had been multiplied by, so as to get just one times the variable.
The above is the approach for linear equations (no variables multiplied by themselves or any other variables). For quadratic equations, the approach is similar, but different, often to put the equation in "standard form" and solve it using a formula for the solution.
One key to algebra is to keep the equal sign sacred. Never violate it. Make sure it is always true that what is on one side is equal to what is on the other side. (It may look like things are being moved from one side to the other, and they are. But note that we do it by performing the same operation on both sides of the equal sign, so the two sides of the equation remain equal.)
It is always a good idea to check your work, preferably in such a way that you don't make the same mistake twice.
3(w-6)-2(4-w)=0
3w-18-8+2w=0
5w-26=0
5w=26
w=26/5