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if 6(2a-1) +8 =14 then find a

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3 Answers

6(2a - 1) + 8 = 14;

12a - 6 + 8 = 14;

12a + 2 = 14;

12a = 12;

a = 1.

6(2a - 1) + 8 = 14

12a - 6 + 8 = 14

12a + 2 = 14

12a + 2 - 2 = 14 - 2

12a = 12

12a/12 = 12/12

a = 1

When solving for a variable, the ultimate goal is to get the desired variable on one side of the equal sign and everything else on the other side. In order to do this, you need to do what's called the "inverse operation" of everything next do the desired variable (for multiplication, this would be division; for addition, it would be subtraction; and vice versa). You need to perform the inverse operations in the reverse order of operations (SADMEP as opposed to PEMDAS), and anything you do to one side you need to do to the other.

We're given that 6(2a-1) +8 =14. The first task in our reverse order of operations is addition and subtraction. On the left-hand side, 8 is being added. This means we need to perform the inverse of this addition: subtraction. Therefore we subtract 8 from both sides. +8 and -8 cancel out on the left-hand side. 14 and -8 make 6 on the right-hand side.

We're left with 6(2a-1) = 6. Next in our reverse order of operations we have multiplication and division. On the left-hand side (2a-1) is being multiplied by 6, so we should now do the inverse of that and divide both sides by 6. The 6's cancel out on both sides, leaving 2a-1 =1.

Of the operations left, addition and subtraction come first in reverse order of operations, so we'll do that next. 1 is being subtracted on the left-hand side, so we should now add 1 to both sides. It cancels on the left, and leaves 2 on the right.

Finally, we have 2a = 2. The last operation left is multiplication, so we should divide by 2 on both sides. This leaves a = 1 as our answer.