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3 years ago

Solve the absolute value equation. Check for extraneous solutions: |9x-3|=12

Mathematics

1 answer:

STatiana [176]3 years ago

5 0

ANSWER: x=5/3, -1. Good luck. Hope this suffices.

Explanation for x=-1: |9x-3|=12. Lets take the absolute value brackets away for a sec. Add 3 to both sides 9x-3+3=-12+3, simplify: 9x=-9, divide both sides by nine:9x/9=-9/9. And that means that x=-1.

Explanation for x=5/3: |9x-3|=12. Add 3. 9x-3+3=12+3. Simplify: 9x=15. Divide both sides by 9. 9x/9=15/9. Simplify: x=5/3

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9 burgers and 1 doughnut cost $31.30. 3 doughnuts and 6 burgers cost $26.70. Find the cost of 2 burgers.

kirill [66]

Step-by-step explanation:

Let assume that

Cost of 1 burger = $ x

Cost of 1 doughnuts = $ y

According to statement, 9 burgers and 1 doughnut cost $ 31.30

$\begin{gathered}\sf \: 9x + y = 31.3 \\ \\ \end{gathered}$

$\begin{gathered}\sf\implies \sf \: y = 31.3 - 9x - - - (1) \\ \\ \end{gathered}$

According to statement again, 3 doughnuts and 6 burgers cost $ 26.70

$\begin{gathered}\sf \: 6x + 3y = 26.7 \\ \\ \end{gathered}$

$\begin{gathered}\sf \: 3(2x + y) = 26.7 \\ \\ \end{gathered}$

$\begin{gathered}\sf \: 2x + y = 8.9 \\ \\ \end{gathered}$

On substituting the value of y from equation (1), we get

$\begin{gathered}\sf \: 2x + 31.3 - 9x = 8.9 \\ \\ \end{gathered}$

$\begin{gathered}\sf \: 31.3 - 7x = 8.9 \\ \\ \end{gathered}$

$\begin{gathered}\sf \: - 7x = 8.9 - 31.3 \\ \\ \end{gathered}$

$\begin{gathered}\sf \: - 7x = - 22.4 \\ \\ \end{gathered}$

$\begin{gathered}\bf\implies \: x = 3.2 \\ \\ \end{gathered}$

So,

Cost of 2 burgers = 3.2 × 2 = $ 6.4

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​Solve the absolute value equation. Check for extraneous solutions: |9x-3|=12

Solve the absolute value equation. Check for extraneous solutions: |9x-3|=12