Solve for x: 3|x - 3| + 2 = 14

Mathematics

2 answers:

Xelga [282]2 years ago

7 0

Two solutions,
x=7
x=-1
So, D would be your answer.

PilotLPTM [1.2K]2 years ago

3 0

1 Subtract 22 from both sides
3|x-3|=14-23∣x−3∣=14−2

2 Simplify 14-214−2 to 1212
3|x-3|=123∣x−3∣=12

3 Divide both sides by 33
|x-3|=\frac{12}{3}∣x−3∣=
3

12

4 Simplify \frac{12}{3}
3

12
to 44
|x-3|=4∣x−3∣=4

5 Break down the problem into these 2 equations
x-3=4x−3=4
-(x-3)=4−(x−3)=4

6 Solve the 1st equation: x-3=4x−3=4How?
x=7x=7

7 Solve the 2nd equation: -(x-3)=4−(x−3)=4How?
x=-1x=−1

8 Collect all solutions
x=-1,7x=−1,7

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Find the solution to the system of equations 2x+3y+z=20 3y+5z=12 y-5z=4

podryga [215]

Answer:

x =4 ,y =4 and z =0 is the solution.

Step-by-step explanation:

We shall solve the equations using elimination method

In equation 2 and 3 we can see that coefficient of z in both equations are same with opposite sides , adding equations (2) and (3)

3y+5z = 12

y -5z = 4 adding the equations

___________

4y = 16

dividing both sides by 4

y = $\frac{16}{4}$

y = 4

Plugging the value of y in equation 2 or equation 3 ,we get

3(4) +5z = 12

12+5z = 12

5z = 12-12 or 5z =0 gives z =0

plugging y =4 and z =0 in equation 1

2x+3(4)+ 0 = 20

2x+12 = 20

2x =20-12

2x = 8

x = 8 divided by 2 gives

x =4

therefore solution of the system is given by

x=4 , y =4 and z =0

3 0

3 years ago

Read 2 more answers

Bill and Mary Ann went to the Viola bakery. Bill bought 5 pies and 7 donuts for $12.65. Mary Ann bought 6 of each for $12.30.

sweet [91]

Answer:

Pies=$0.85

Donuts= $1.20

Step-by-step explanation:

In the equation let p stand for the number of pies and d stand for the number of donuts.

To solve this set up 2 equations, one representing bill and the other representing Mary Ann.

Bill's equation is 5p+7d=$12.65.
Mary Ann's equation is 6p+6d=$12.30

Then solve using a system of equations. Systems of equations can be solved using elimination or substitution. I will use substitution. Solve bill's equation for p. This gives you $p=\frac{12.65-7d}{5}$ . Then, you can substitute that into Mary Ann's equation. This looks like $6\cdot \frac{12.65-7d}{5}+6d=12.3$ . Solve for d. Once you solve d=1.20. Finally, substitute 1.20 back into either Bill's or Mary Ann's for d and solve for p. No matter which equation you use p=0.85.