Question

These are so confusing, can someone explain how to do this

Answer 1

4

Explanation:

x/2 +6 = 8

subtract 6 from both sides

x/2 = 2

multiply by the reciprocal of 1/2 which is 2. That cancels out the 2 on the x side and x is equal to 4

Hope that helps

Answer 2

x = 4

Explanation:

The left side of the equation has a variable term (x/2) and a constant term (6).

The right side of the equation has a constant term (8).

This is the form you expect to see for a "two-step" linear equation. It is solved in 2 steps.

Step 1:

Subtract the left-side constant from both sides.

x/2 +6 -6 = 8 -6

x/2 = 2 . . . . . simplify

Step 2:

Multiply both sides of the equation by the reciprocal of the coefficient of x. The coefficient of x is 1/2. Its reciprocal is 2/1 = 2. When you multiply both sides by 2, you get ...

2(x/2) = 2(2)

x = 4 . . . . . . simplify

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Additional comment

The idea of a multiplicative inverse (reciprocal) is that a number multiplied by its reciprocal is 1.

`(2)/(1)*(1)/(2)=(2)/(2)=1`

1 is the "identity element" for multiplication. That means whatever you multiply by 1 retains its original identity. Multiplying x by 1 gives x.

When we solve an equation of this sort, we use these properties of multiplication (inverse, identity element) to "get rid of" the coefficient of x.

As always, the rules of equality say that whatever you do to one side of the equation must also be done to the other side. So, when we multiply x/2 by 2, we must also multiply the other side of the equation by 2.

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Don't let the presentation of the x-term throw you. It can be written several ways that all mean the same thing.

(1/2)x . . . . with or without the parentheses

0.5x

x/2