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

Question

Solve each linear equation. See Examples 1–3. 2 [x - (4 + 2x) + 3] = 2x + 2

Accepted Answer

Hello, everyone. We are asked to find the solution for the equation given below our equation is five multiplied by open bracket. Three X minus open parentheses. Nine plus 17 X closed parentheses plus 19. Close bracket equals negative 61 X plus 23. Our answer choices are a three B negative three C negative 27 divided by 161. D one third. Ok. So I will start by rewriting this. So five multiplied by open bracket. Three X minus open parentheses. Nine plus 17 X closed parentheses plus 19, close bracket equals negative 61 X plus 23. So I'm gonna start with my innermost set of grouping symbols. So that's my parentheses directly outside of my parentheses. I have a minus sign. I'm gonna treat that as if this is a negative one and we're gonna distribute negative one into those parentheses. I'm going to rewrite the equation with nothing else changed except for multiplying in the negative one. So I also have five multiplied by the bracket and then three X and this will be minus nine minus 17 X plus 19. Close bracket equals negative 61 X plus 23. So now I wanna combine my like terms within the brackets. I have a three X and a negative 17 X that I'll combine and I have a negative nine and a positive 19. So when I do so the five stays on the outside multiplied by the bracket and then combining my X terms, I have negative 14 X, combining my constants, I get a positive 10. So plus 10 close bracket equals negative 61 X plus 23. So next, we are going to multiply the five into the bracket. So we're using the distributive property again. So we will have five multiplied by negative 14 X which will give us negative 70 X and then five multiplied by 10 will be plus equals negative 61 X plus 23. OK. So now we have to decide which direction do we want to move our variables in which direction do we want to move our constants in? I'm going to start by moving my variable and I'm gonna add 61 X to both sides. That way I move my variables to the left. And when I do so I have negative nine X plus 50 equals 23. Then I'm gonna subtract 50 from both sides to try to get the X by itself. And this will give me negative nine X equals negative 27. And then I'll divide both sides by negative nine to get the X by itself. And we find that X equals three. So X equals three would match to answer choice. A, have a nice day.

Solve each linear equation. See Examples 1–3. 2 [x - (4 + 2x) + 3] = 2x + 2

Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations

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