Six hundred four thousand sixteen
1. −2x−4=20+6x
Step 1: Simplify both sides of the equation.
−2x−4=20+6x
−2x+−4=20+6x
−2x−4=6x+20
Step 2: Subtract 6x from both sides.
−2x−4−6x=6x+20−6x
−8x−4=20
Step 3: Add 4 to both sides.
−8x−4+4=20+4
−8x=24
Step 4: Divide both sides by -8.
−8x/−8=24/−8
x=−3
Answer:
x=−3
3. (x/4)*(4)=(9)*(4)
x=36
Answer:
x=36
4.
2(5x−1)=3x+5
Step 1: Simplify both sides of the equation.
2(5x−1)=3x+5
(2)(5x)+(2)(−1)=3x+5(Distribute)
10x+−2=3x+5
10x−2=3x+5
Step 2: Subtract 3x from both sides.
10x−2−3x=3x+5−3x
7x−2=5
Step 3: Add 2 to both sides.
7x−2+2=5+2
7x=7
Step 4: Divide both sides by 7.
7x/7=7/7
x=1
Answer:
x=1
5.
8−2(3x−4)+2x=5(x+6)+4
Step 1: Simplify both sides of the equation.
8−2(3x−4)+2x=5(x+6)+4
8+(−2)(3x)+(−2)(−4)+2x=(5)(x)+(5)(6)+4(Distribute)
8+−6x+8+2x=5x+30+4
(−6x+2x)+(8+8)=(5x)+(30+4)(Combine Like Terms)
−4x+16=5x+34
−4x+16=5x+34
Step 2: Subtract 5x from both sides.
−4x+16−5x=5x+34−5x
−9x+16=34
Step 3: Subtract 16 from both sides.
−9x+16−16=34−16
−9x=18
Step 4: Divide both sides by -9.
−9x/−9=18/−9
x=−2
Answer:
x=−2
Answer:
part a: -40 < x < 140
part b: open circles on both -40 and 140 with an arrow from each pointing inward. (towards zero). the solutions represent temperatures that will keep the gas in liquid form.
part c: it will freeze because -49 is less than -40, and therefore not a solution to the inequality.
explanation
a. x must be greater than -40 and less than 140 as outlined in the problem. so x > -40 and x < 140
b. open circles are non inclusive, and we do not include -40 or 140 because the gas will not be a liquid at those temps.
