Solve the Equation. 3 ( 2 − 5 x ) = 4 x + 25 3\left(2-5x\right)=4x+25

Hey, everyone. Let's take a look at this practice problem. So I wanna solve this linear equation, 3 times 2 minus 5 x is equal to 4x +25. So let's go ahead and start with step 1, which is to distribute our constants. So here I have this 3 that needs to get distributed to both my 2 and my negative 5 x, which will give me 6 minus 15 x. And then there's nothing that needs to get distributed on that right side. So it will stay the same, 4x plus 25. So step 1 is done. Moving on to step 2, we need to go ahead and combine our like terms. Now on both sides of my equation, it doesn't look like I have any like terms that need to get combined. So step 2 is done as well, and I can move on to step 3, which is to put my constants on one side and all of my terms with x on the other. So I wanna go ahead and move this 4 x to the left and move my 6 over to the right with that 25. So in order to do that, I need to subtract 4 x from both sides, of course, leaving it to cancel on that left or on that right side, and then I need to subtract my 6 as well. So, of course, cancel there. Then I'm left with negative 15x minus 4x, which will give me negative 19x is equal to 25 minus 6, which is positive 19. So step number 3 is done, and our next step is going to be to isolate x. So here I have a negative 19 multiplying my x. I'm gonna go ahead and divide by negative 19 in order to get rid of that. So, of course, I need to do that to the other side as well, and it will cancel, leaving me, of course, with x. And then that's equal to 19 divided by negative 19, which is negative one. So this is my solution, x equals negative 1, and step 4 is complete. But we, of course, have one final step, which is to check our solution in our original equation. So let's go ahead and do that. 3 times two minus five times x, which we got is negative one. So I'm gonna replace it in my equation, is equal to 4 times negative one plus twenty 5. And let's go ahead and simplify that. So I have 3 times 2 minus or, well, negative 5 times negative one actually gives me positive 5, so this will become plus 5. And that's equal to 4 times negative one gives me negative 4 plus 25. Simplifying that further, on my left side, I'll have 3 times 7 is equal to negative 4 plus 25, which is 21. Very last step, my 3 and my 7 multiplying each other will give me 21, and that's equal to 21. Now this is, of course, a true statement, so that means that my solution x equals negative one is correct. That's all for this one. Let me know if you have questions.