Solve: 6|1 – 2x| — 7 = 11.

Question

Accepted Answer

Hello everybody. I have everything right today that we're going to look at this question that states solve the equation for X where our equation is 11, multiplying the absolute value of four X plus one and outside of the absolute value bars plus three, that'll be equal to 25. Now, the s provided are A X equals negative two and one half B X equals negative three divided by four and 4/1 4th C X is equal to negative one third and two thirds. N D X equals to negative four and 3/4. No. So they ask us to solve for X. So we have to treat this like any other question where we have to isolate the variable. So the first thing I'll do is move the plus three from the left hand side of our equation to the right hand side by subtracting it. And that'll leave us with 11 multiplying the absolute value of four X plus one. And now that will be equal to 25 minus three, which is 22. Now, the next thing we'll do to isolate the X is we'll treat the absolute value bars like if they were parentheses. So the 11 is multiplying whatever is inside the absolute value bars. So to get rid of the 11, on the left hand side, we have to divide both sides by 11, which means on the left hand side, it will now be left with the absolute value of four X plus one. And that'll be equal to 22 divided by 11, which is two. Now is when we saw Rex. Now, instead of treating it now like parentheses, we have to treat it like absolute value. Now, absolute value, we know that anything that comes out of the absolute value bars will turn positive. So we have to turn, we have to solve for two different equations. Now we'll have four X plus one equals two and we'll have four X plus one equals negative two. Because even if our equation for X plus one equals negative two, it will be inside absolute value bars. And therefore that negative two will turn positive. So that will also be a solution for our equation. So let's solve the positive answer first for the positive two first. So we'll have four X plus one equals two. So we'll move the one over from the left hand side to the right hand side by subtracting. And we'll be left with four X equals two minus one, which is one and not to isolate the X, we divide both sides by four. So I have that X is equal to one divided by four or 1/4. Now, for the other answer where we have the negative two answer, we do the same thing. We move the one over from the left hand side to the right hand side and we'll have four, X is equal to negative two minus one, which is negative three. And then we divide both sides by four to isolate the X and we'll be left with X is equal to negative three, divided by four or negative 3/4. And those will be our two answers for this question. And if we look at our answer choices, we see that this matches up with answer choice B so I hope that was helpful. And until next time.

Solve: 6|1 – 2x| — 7 = 11.

Key Concepts

Absolute Value

Linear Equations

Isolating the Variable

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