Quick Question Related To Properties of Radicals

[GetThroughDiffEq]

Say we have to solve for 'x' -in the problem 2√x - 2 = 10.

Explain to me why do we add 2 to both sides and then divide by 2 on both sides?

Bonus: Could you make a real life example out of a similar problem?

 

[Steven G]

\(\displaystyle 2\sqrt{x}\) is an unknown value but we know if we subtract 2 from it we get 10. Well 12 - 2 =10, so we let 2\(\displaystyle \sqrt{x}\)=12

Now \(\displaystyle 2\sqrt{x}\)=12 and we know that 2*6=12 so \(\displaystyle \sqrt{x}\)= 6. Now we know \(\displaystyle \sqrt{36}\) = 6, so x= 36.

Just use common sense logic!

 

[Otis]

… solve for 'x' … 2√x - 2 = 10

Explain to me why do we add 2 to both sides and then divide by 2 on both sides? …

Those are the most basic steps taught in Beginning Algebra. It's how we begin to isolate x to one side of the equation (that is, solve for symbol x).

Are you studying math on your own? Or, has it been awhile, since you studied introductory algebra? You may want to consider reviewing topic videos online, from a structured introduction to beginning algebra (eg: Khan Academy).

2∙√x - 2 = 10

To begin isolating x, we first isolate the radical √x. In other words, on the left-hand side we don't want that subtraction of 2 OR that multiplication by 2, so we take steps to eliminate them. We eliminate the subtraction of 2 by adding 2 to each side. Addition is the inverse of subtraction.

2∙√x - 2 + 2 = 10 + 2

Simplify

2∙√x = 12

We eliminate the multiplication by 2 using the inverse of multiplication, which is division. Divide each side by 2.

(2∙√x)/2 = 12/2

Simplify

√x = 6

We have isolated the radical containing x, but we're not done isolating x. To get rid of the radical sign, square both sides.

(√x)² = 6²

Simplify

x = 36

Questions about any of this?

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