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ASAP 50 POINTS WILL MARK BRAINLIEST


Solve for x: −3|2x + 6| = −12

Solve for x: |2x + 6| − 4 = 20

Solve for x: |x| − 8 = −5

Compare and Contrast: Two equations are listed below. Solve each equation and compare the number of solutions.

Equation 1 Equation 2
|5x + 6| = 41 |2x + 13| = 28
Solve for x: −4|x + 5| = −16
The minimum and maximum temperature on a cold day in Lollypop Town can be modeled by the equation below:

2|x − 6| + 14 = 38

What are the minimum and maximum temperatures for this day?

Respuesta :

calculista

Answer:

Part 1) The solutions are x=-1, x=-5

Part 2) The solutions are x=-15, x=9

Part 3) The solutions are x=-3, x=3

Part 4) The solutions of equation 1 are x=-9.4,x=7 and the solutions of the equation 2 are x=-20.5, x=-7.5

Part 5) The solutions are x=-9, x=-1

Part 6) The minimum temperature is x=-6° and the maximum temperature is x=18°

Step-by-step explanation:

Part 1) we have

Solve for x

[tex]-3\left|2x+6\right|=-12[/tex]

Simplify

Divide by -3 both sides

[tex]\left|2x+6\right|=4[/tex]

Find out the first solution (case positive)

[tex]+(2x+6)=4[/tex]

[tex]2x=4-6[/tex]

[tex]2x=-2[/tex]

[tex]x=-1[/tex]

Find out the second solution (case negative)

[tex]-(2x+6)=4[/tex]

Multiply by -1 both sides

[tex](2x+6)=-4[/tex]

[tex]2x=-4-6[/tex]

[tex]x=-5[/tex]

Part 2) we have

Solve for x

[tex]\left|2x+6\right|-4=20[/tex]

Simplify

Adds 4 both sides

[tex]\left|2x+6\right|=24[/tex]

Find out the first solution (case positive)

[tex]+(2x+6)=24[/tex]

[tex]2x=24-6[/tex]

[tex]2x=18[/tex]

[tex]x=9[/tex]

Find out the second solution (case negative)

[tex]-(2x+6)=24[/tex]

Multiply by -1 both sides

[tex](2x+6)=-24[/tex]

[tex]2x=-24-6[/tex]

[tex]2x=-30[/tex]

[tex]x=-15[/tex]

Part 3) we have

Solve for x

[tex]\left|x\right|-8=-5[/tex]

Simplify

Adds 8 both sides

[tex]\left|x\right|=3[/tex]

Find out the first solution (case positive)

[tex]+(x)=3[/tex]

[tex]x=3[/tex]

Find out the second solution (case negative)

[tex]-(x)=3[/tex]

Multiply by -1 both sides

[tex]x=-3[/tex]

Part 4) Solve each equation and compare the number of solutions

Equation 1

[tex]\left|5x+6\right|=41[/tex]

Find out the first solution (case positive)

[tex]+(5x+6)=41[/tex]

[tex]5x=41-6[/tex]

[tex]5x=35[/tex]

[tex]x=7[/tex]  

Find out the second solution (case negative)

[tex]-(5x+6)=41[/tex]

Multiply by -1 both sides

[tex](5x+6)=-41[/tex]

[tex](5x+6)=-41-6[/tex]

[tex]5x=-47[/tex]

[tex]x=-47/5=-9.4[/tex]

Equation 2

[tex]\left|2x+13\right|=28[/tex]

Find out the first solution (case positive)

[tex]+(2x+13)=28[/tex]

[tex]2x=28-13[/tex]

[tex]2x=15[/tex]

[tex]x=7.5[/tex]

Find out the second solution (case negative)

[tex]-(2x+13)=28[/tex]

Multiply by -1 both sides

[tex](2x+13)=-28[/tex]

[tex]2x=-28-13[/tex]

[tex]2x=-41[/tex]

[tex]x=-20.5[/tex]

Each equation has two solutions

Part 5) Solve for x

[tex]-4\left|x+5\right|=-16[/tex]

Simplify

Divide by -4 both sides

[tex]\left|x+5\right|=4[/tex]  

Find out the first solution (case positive)

[tex]+(x+5)=4[/tex]

[tex]x=4-5[/tex]

[tex]x=-1[/tex]

Find out the second solution (case negative)

[tex]-(x+5)=4[/tex]

Multiply by -1 both sides

[tex](x+5)=-4[/tex]

[tex]x=-4-5[/tex]

[tex]x=-9[/tex]

Part 6) What are the minimum and maximum temperatures for this day?

we have

[tex]2\left|x-6\right|+14=38[/tex]

Simplify

Subtract 14 both sides

[tex]2\left|x-6\right|=24[/tex]

Divide by 2 both sides

[tex]\left|x-6\right|=12[/tex]

Find out the first solution (case positive)

[tex]+(x-6)=12[/tex]

[tex]x=12+6[/tex]

[tex]x=18[/tex]

Find out the second solution (case negative)

[tex]-(x-6)=12[/tex]

Multiply by -1 both sides

[tex](x-6)=-12[/tex]

[tex]x=-12+6[/tex]

[tex]x=-6[/tex]

therefore

The minimum temperature is x=-6° and the maximum temperature is x=18°

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