Solve each linear equation. See Examples 1–3. -4 (2x - 6) + 8x...

Question

Solve each linear equation. See Examples 1–3. -4 (2x - 6) + 8x = 5x + 24 + x

Accepted Answer

Welcome back. Everyone in this problem, we want to find a solution for the equation seven X minus 19, all multiplied by negative eight plus eight, X equals five, X plus 152 plus seven X. For our answer choices, A is zero, B is negative 60 C is 60 D is no solution. Now, what are we trying to do here? Well, we want the solution for the equation. In other words, we just want to figure out what X equals. And if we're going to do that, that means we can try to simplify and balance our equation as much until we work it down to get only X. So let's go ahead and do that. So we have negative eight open parenthesis, seven X minus 19, close parenthesis plus eight X equals five X plus 152 plus seven X. Now, before we start, let's distribute that will make solving our problem easier. Now, negative eight multiplied by seven X, that's negative 56 X and the negative eight multiplied by negative 19 is a positive 152. Now, if you notice the next step logically is to try and get our like terms together and we have tons of like terms here. So let's see if we can combine those. So notice that we have X terms negative 56 X plus eight X. And when we combine those, we get negative 48 XX and that's on our left hand side and on our right hand side, we have five X and seven X. And when we combine those five X plus seven X, that would be 12 X plus 152. Now, we can simplify it even further because both sides have 152. So if we, if we add or if we subtract rather, if we subtract 152 from both sides, then on the left hand side, we'll have negative 48 X. And on the right hand side, we'll have 12 X, we still have some more to go because we can subtract 12 X from both sides. OK? 12 X minus 12 X leaves us with zero on the right hand side and negative 48 X minus 12 X equals negative 60 X. Now, if negative 60 X equals zero, that means to get X, we can divide both sides by negative and nega let me sorry, negative 60. We write that properly. No negative 60 factors out of the left hand side and leaves us with X and zero divided by negative 60 equals zero. Therefore X equals zero. And if we look back in our answer choices that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

Solve each linear equation. See Examples 1–3. -4 (2x - 6) + 8x = 5x + 24 + x

Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations

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