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°
