Solve the following equations.(B) ∣3x−5∣−6=2\left|3x-5\right|-6=2

x = { 13 3 , − 1 } x=\left\lbrace\frac{13}{3},-1\right\rbrace

Solve the following equations. ( B ) ∣ 3 x − 5 ∣ − 6 = 2 \left|3x-5\right|-6=2

Welcome back. For this problem, we'd like to solve the equation absolute value of three x minus five minus six equals two. The first step to solving an absolute value equation is to isolate the absolute value on one side of the equation. In our equation, we have the absolute value of something minus six equals two. So we wanna get rid of this minus six so the absolute value will be alone on the left side of the equation, which means our first step is going to be adding six to both sides of the equation, which will cancel the minus six on the left, leaving us with absolute value of three x minus five is equal to two plus six, which is eight. Now that we have absolute value of something is equal to a positive number, we can rewrite this one equation as two equations without the absolute value, where the first one takes the thing in the absolute value, three x minus five, and sets it equal to our a, which in this case is eight. And the second takes that three x minus five and sets it equal to negative a, which is negative eight. Now let's solve our first equation, three x minus five equals eight. The first step is going to be adding five to both sides of the equation, which will cancel out the minus five on the left, leaving us with three x equals eight plus five, which is 13. Next, we can divide both sides of the equation by three to get rid of our coefficient of three, leaving us with just x on the left, equals 13 divided by three, which is 13 thirds. That's our first solution, but let's solve our second equation. We have three x minus five equals negative eight. We want to get rid of this minus five on the left so we can add five to both sides of the equation. It will cancel with the minus five on the left, leaving us with three x, and on the right, we have negative eight plus five, which is negative three. Then, we can divide both sides of the equation by three to cancel the coefficient of three on the left, leaving us with x equals negative three divided by three, which is negative one. So we get our second solution as x equals negative one. We can plug in both of those values for x into the original equation, and we'll get a true statement. So our solution set includes both of those solutions, 13 thirds and negative one. Great work.

Solve the following equations. ( B ) ∣ 3 x − 5 ∣ − 6 = 2 \left|3x-5\right|-6=2

x = { 13 3 , − 1 } x=\left\lbrace\frac{13}{3},-1\right\rbrace

x = { − 13 3 , 1 } x=\left\lbrace-\frac{13}{3},1\right\rbrace

x = { 3 , − 1 3 } x=\left\lbrace3,-\frac13\right\rbrace

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Multiple Choice

Solve the following equations.
(B) $∣ 3 x - 5 ∣ - 6 = 2$

$x = {\frac{13}{3}, - 1}$

$x = {- \frac{13}{3}, 1}$

$x = {3, - \frac{1}{3}}$

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Verified step by step guidance

Start with the given equation involving the absolute value: $\left|3x - 5\right| - 6 = 2$.

Isolate the absolute value expression by adding 6 to both sides: $\left|3x - 5\right| = 2 + 6$.

Simplify the right side to get $\left|3x - 5\right| = 8$.

Recall that if $\left|A\right| = B$, where $B > 0$, then $A = B$ or $A = -B$. So set up two equations: \$3x - 5 = 8$ and $3x - 5 = -8$.

Solve each linear equation separately for $x$: - For \$3x - 5 = 8$, add 5 to both sides and then divide by 3. - For $3x - 5 = -8$, add 5 to both sides and then divide by 3.

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