what is 3x-12=14?
Ok bob, what happens if we add 12 to both sides? Why can we do this?
After that step, what happens if we divide both sides by 3? Why is that allowable? What value do we get for x then?
3x-12=14
3x-12=14
+12=+12
3x=26
26/3x
x=8.7
To solve the equation 3x - 12 = 14, follow these steps:
Step 1: Add 12 to both sides of the equation.
3x - 12 + 12 = 14 + 12
As a result, the -12 on the left side cancels out:
3x = 26
Now, let's address why we can add 12 to both sides of the equation.
In algebra, you can perform the same operation to both sides of an equation without changing the equality. Adding 12 to both sides is an example of using the addition property of equality. This property states that if a = b, then a + c = b + c, where 'c' is any real number. By applying this property, we keep the equation balanced.
Moving on to Step 2: Divide both sides of the equation by 3.
(3x) / 3 = 26 / 3
On the left side, the 3s cancel out, leaving only x:
x = 8.6667 (rounded to four decimal places)
Now let's discuss why we can divide both sides by 3.
Similar to the addition property, the division property of equality allows us to divide both sides of an equation by the same non-zero number. It states that if a = b and c is a non-zero number, then a/c = b/c. By dividing both sides by 3, the equation remains balanced.
Therefore, the solution to the equation is x ≈ 8.6667.