Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. 5 x + 17 = 8 x + 12 − 3 ( x + 4 ) 5x+17=8x+12-3\left(x+4\right) 5 x + 17 = 8 x + 12 − 3 ( x + 4 )

Hey, y'all. Let's take a look at this practice problem. We wanna solve this linear equation and then state whether it is an an identity, conditional, or inconsistent equation. We have 5 x plus 17 is equal to 8 x plus 12 minus 3 times x plus 4. So let's go ahead and start solving. Now step 0 is to multiply by our least common denominator to eliminate fractions, but here, I don't have any fractions, so I don't have to worry about that step 0. It's done. Step 1 is then to distribute any constants that I have. And I do have a constant here, so let's go ahead and distribute that. I have this 3 right here that needs to get distributed to both the x and the 4 or, well, this negative 3 that needs to get distributed. Now the left side of my equation doesn't have any constants, so I'm gonna go ahead and keep it the same and then fill in my right side, 8 x +12. And then distributing that negative 3, I get negative 3xminus12. So step 1 is done. I've distributed my constant. Let's move on to step 2, which is to combine our like terms. Now it looks like we have quite a few like terms that we need to combine here. So, again, that left side of my equation doesn't have anything that I need to combine, so I can keep it the same. And then I can move on to combining like terms on my right side. So I have this 8 x and I have a negative 3 x. I also have this 12 and a negative 12. So combining this 8 x and this 3 negative 3 x, I get positive 5x. And then combining my 12 and my negative 12, 12 minus 12 will give me 0. So I can stick that 0 there, but really doesn't mean anything because it's just 0. So I'm not even going to worry about it. So now my equation that I have left is 5x+eseventeenequals5x. So step 2 is done. Moving on to step 3, grouping our terms with x on one side and constants on the other. Now since I only have one constant and it's already on the left side, I'm going to keep it there and move this 5 x over. So to do that, I need to subtract 5 x from both sides. So, of course, cancel on that left side. I'm left with 17. But when I go to subtract that 5 x over here, I end up with 5 x minus 5 x, which will give me 0. Now don't worry. We didn't do anything wrong here. We just got a false statement, 17 equals 0, which tells us that we have an inconsistent equation because this is definitely not true. It's definitely not gonna work with any number that I plug in. No matter what, 17 will never be equal to 0, so it is an inconsistent equation with no solution. That's all for this one. Let me know if you have questions.

Solve the equation. Then state whether it is an identity, conditi...

0. Review of College Algebra4h 43m

1. Measuring Angles39m

2. Trigonometric Functions on Right Triangles2h 5m

3. Unit Circle1h 19m

4. Graphing Trigonometric Functions1h 19m

5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m

6. Trigonometric Identities and More Equations2h 34m

7. Non-Right Triangles1h 38m

8. Vectors2h 25m

9. Polar Equations2h 5m

10. Parametric Equations1h 6m

11. Graphing Complex Numbers1h 7m

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.
$5x+17=8x+12-3\left(x+4\right)$