In Exercises 51–58, solve each equation. Express the solution in ...

Question

In Exercises 51–58, solve each equation. Express the solution in scientific notation.x-(7.2X10¹⁸)=8.4X10¹⁸

Accepted Answer

Welcome back. I am so glad you're here. We are given this practice problem and we're told for the following equation work out the value of X, right. The final answer in scientific notation, the equation that we're given is X minus 5.9 times 10 raised to the 15th and that is equal to 7.1 times 10, raised to the 15th. Our answer choices are a negative 1.3 times 10 to the 16th. B, 1.3 times 10 to the 16th. C negative 1.3 times 10 to the 15th and D positive 1.3 times 10 to the 15th. Alright, I want to point out that the X that we are trying to work the value out for is this first one, the other exes are denoting multiplication. And we can see that recalling the order of operations, the multiplication happens first here. So this minus 5.9 times 10 to the 15th. That's happening before we are taking X minus the 5.9 times 10 to the 15th. And so we can treat this 5.9 times 10 to the 15th as a unit. And what we can do is we can add it to both sides of the equation. We can add 5.9 times 10 to the 15th. And what we do to one side, we do to the other side. And then we have the X by itself on the left hand side, which is what we want. Now, it's just a matter of simplifying on the right hand side, I'm going to write this out first, we have 7.1 times 10 to the 15th plus 5.9 times 10 to the 15th. We are adding these two. And what we notice is that they are both being multiplied times 10 to the 15th. They have the same base the 10 and the same exponent the 15th. So what we can actually do is combine, we can add because the operation here is adding these numbers here in front that are both being multiplied by the 10 to the 15th. So we can take 7.1 plus 5.9. And when we add those together, we have 13. And what we're saying is we have 13 units times 10 to the 15th because both the 7.1 and the 5.9 were being multiplied by 10 to the 15th. That's still equal to X. Well, we almost have our final answer in scientific notation. However, we recall from previous lessons that we have to have one number between one through nine, followed by a decimal point for scientific notation right now, the decimal point is after the three. So we're moving it to the left one. And whenever we move a decimal point to the left one unit, we are raising our exponent for the 10 to the, that exponent gets raised. And because it's moving to the left one unit, it's getting raised by one. So we're taking that 15 exponent plus one, well, 15 plus one is 16. So we have 1.3 times 10 to the 16th. And this is our answer in scientific notation, we look at our answer choices for 1.3 times 10 to the 16th. And that matches with answer choice B well done. We'll catch you on the next one.

In Exercises 51–58, solve each equation. Express the solution in scientific notation.x-(7.2X10¹⁸)=8.4X10¹⁸

Key Concepts

Scientific Notation

Solving Linear Equations

Combining Like Terms

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