Mathematics, 03.07.2019 19:30 lucky1940

Your friend says that the absolute value equation |3x+8|−9=−5 has no solution because the constant on the right side of the equation is negative. is your friend correct? explain.

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Answer from: hamptonjeleesa

No friend is wrong

Step-by-step explanation: you actually get two answers. After you isolate the absolute value then you take the positive and negative number of what it's set equal too.

|3x + 8| - 9 = -5 add 9 to isolate the absolute value

|3x + 8| = 4

Now set two equations because the abosulte value has two answers.

|3x + 8| = 4. and |3x + 8| = -4

Solve these by removing the absolute value bars.

3x = -4. 3x = -12

x = -4/3. X = -4

Answer from: rhucke99121

$Solution, solve\:for\:x,\:\left|3x+8\right|-9=-5\quad :\quad x=-4\quad \mathrm{or}\quad \:x=-\frac{4}{3}$

Steps:

$\left|3x+8\right|-9=-5$

$\mathrm{Add\:}9\mathrm{\:to\:both\:sides},\\\left|3x+8\right|-9+9=-5+9$

$\mathrm{Simplify},\\\left|3x+8\right|=4$

$|f\left(x\right)|=a\quad \Rightarrow \:f\left(x\right)=-a\quad \mathrm{or}\quad \:f\left(x\right)=a,\\3x+8=-4\quad \quad \mathrm{or}\quad \:\quad \:3x+8=4$

$3x+8=-4,\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides},\\3x+8-8=-4-8,\\\mathrm{Simplify},\\3x=-12,\\\mathrm{Divide\:both\:sides\:by\:}3,\\\frac{3x}{3}=\frac{-12}{3},\\\mathrm{Simplify},\\x=-4$

$3x+8=4,\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides},\\3x+8-8=4-8,\\\mathrm{Simplify},\\3x=-4,\\\mathrm{Divide\:both\:sides\:by\:}3,\\\frac{3x}{3}=\frac{-4}{3},\\\mathrm{Simplify},\\x=-\frac{4}{3}$

$Combine\:the\:ranges,\\x=-4\quad \mathrm{or}\quad \:x=-\frac{4}{3}$

$\mathrm{The\:Correct\:Answer\:is\:No\:They\:Are\:Not\:Correct}$

$\mathrm{Hope\:This\:Helps!!!}$

$\mathrm{-Austint1414}$

Answer from: saykblahwah309

Hello from MrBillDoesMath!

Your friend is incorrect

Discussion:

| 3x + 8 | -9 = -5 => ( add 9 to both sides)

| 3x + 8 | -9 + 9 = -5 + 9 =>

| 3x + 8 | = 4 =>

3x +8 = 4 or 3x + 8 = -4 =>

x = -4/3 or x = -4

Thank you,

MrB

Answer from: harleymichaelbp74jsq

no, bescause -9 is outside of the absolute value symbols. So whatever is in the absolut value symbols will equal 4 or -4(absolute value symbols making it 4) then -9 will make it -5.

Step-by-step explanation:

Answer from: ani61

No, because u add 9 to both sides to leave what's in the absolute value brackets alone so u get l3x+8l=4.Since the sum is positive then it has a solution.

Answer from: kekoanabor19

No, ur friend is not correct

| 3x + 8 | - 9 = -5u have to get the absolute value (and everything in it) on one side of the equal sign, and everything else on the other side. So we have to get that -9 across the equal sign by adding 9 to both sides
| 3x + 8 } = -5 + 9
| 3x + 8 | = 4...so that number is not negative anymore
now u can set up ur 2 equations and solve for x...ur 2 equations would be:
3x + 8 = 4 and 3x + 8 = -4...so there will be 2 solutions

** if that -9 would not have been there, then ur friend would have been correct

Answer from: savannahvargas512

The question doesn’t make sense

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