Mathematics, 09.07.2019 06:30 shayshayyy41

Solve 5x-4 = |2x+1|. check for extraneous solutions.

Answers: 1

Show answers

Answers

So firstly, we have to break down this equation into two since it's an absolute value equation. Break down the equation as such: $5x-4=2x+1\ \textsf{and}-(5x-4)=2x+1$ . Let's start with the first equation:

Firstly, subtract 2x on both sides of the equation: 3x-4=1

Next, add 4 on both sides: 3x=5

Lastly, divide both sides by 3 and your first answer will be $x=\frac{5}{3}$

Next, let's solve the other equation. Firstly, distribute the minus sign to (5x - 4) (think of the minus sign as -1): -5x+4=2x+1

Next, add 5x to both sides: 4=7x+1

Next, subtract 1 on both sides: 3=7x

Lastly, divide both sides by 7 and your second answer will be $\frac{3}{7}=x$

Now, an extraneous solution is a solution that is found in the equation, but does not hold true when plugged back into the equation. To check if either of our solutions are extraneous, plug them back into the original equation and solve:

Starting with 5/3, firstly plug the value back into the equation:

$5\times \frac{5}{3}-4=|2\times \frac{5}{3}+1|$

Next, solve the multiplication:

$\frac{25}{3}-4=|\frac{10}{3}+1|$

Next, to be able to solve the addition (10/3 + 1/1) and subtraction (25/3 - 4/1), we need to find the LCD, or lowest common denominator, of 3 and 1. To find the LCD, list the multiples of the two and the lowest one they share is their LCD. In this case, their LCD is 3. Multiply both sides of 1/1 and -4/1 by 3/3:

$\frac{1}{1}\times \frac{3}{3}=\frac{3}{3}\\\\-\frac{4}{1}\times \frac{3}{3}=-\frac{12}{3}\\\\\frac{25}{3}-\frac{12}{3}=|\frac{10}{3}+\frac{3}{3}|$

Next, solve the addition and subtraction:

$\frac{13}{3}=\frac{13}{3}$

Now since 13/3 = 13/3 is true, this means that 5/3 is a non-extraneous solution.

Now, let's plug in our other solution 3/7 into the equation:

$5\times \frac{3}{7}-4=|2\times \frac{3}{7}+1|$

Firstly, solve the multiplications:

$\frac{15}{7}-4=|\frac{6}{7}+1|$

Next, find the LCD of 1 and 7. In this case, it's 7. Multiply both sides of -4/1 and 1/1 by 7/7:

$\frac{1}{1}\times \frac{7}{7}=\frac{7}{7}\\\\-\frac{4}{1}\times \frac{7}{7}=-\frac{28}{7}\\\\\frac{15}{7}-\frac{28}{7}=|\frac{6}{7}+\frac{7}{7}|$

Next, solve the addition and subtraction:

$-\frac{13}{7}=\frac{13}{7}$

Since -13/7 is not equal to 13/7, this means that 3/7 is an extraneous solution.

Answer from: Quest

Just turn the whole gym into pie

Answer from: Quest

answer: yes i agree that you should not put it on/p>

step-by-step explanation: the reason for this is that it wastes other peoples time and also make them fail as well and that is never good.

Another question on Mathematics

Mathematics, 21.06.2019 14:50

Which equations represents circles that have a diameter of 12 units and a center that lies on the y-axis? check all that apply

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

How do the definitions, properties, and postulates you've learned about line segments, parallel lines, and angles to define the shapes of polygons

Answers: 1

Answer

Mathematics, 21.06.2019 21:10

For each sentence below, find the value of x that makes each sentence true. (515) 5 = 25* x= (813)2 = 4* x=

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

22. catie is starting a babysitting business. she spent $26 to make signs to advertise. she charges an initial fee of $5 and then $3 for each hour of service. write and solve an inequality to find the number of hours she will have to babysit to make a profit. interpret the solution.!

Answers: 1

Answer

You know the right answer?

Solve 5x-4 = |2x+1|. check for extraneous solutions....

Questions