1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sasho [114]
3 years ago
8

A.)List the 4 steps outlined in the lesson on solving equations.

Mathematics
1 answer:
aleksley [76]3 years ago
7 0
1.) Solve for x:
5 x + 7 = 3 x + 21

Subtract 3 x from both sides:
(5 x - 3 x) + 7 = (3 x - 3 x) + 21

5 x - 3 x = 2 x:
2 x + 7 = (3 x - 3 x) + 21

3 x - 3 x = 0:
2 x + 7 = 21

Subtract 7 from both sides:
2 x + (7 - 7) = 21 - 7

7 - 7 = 0:
2 x = 21 - 7

21 - 7 = 14:
2 x = 14

Divide both sides of 2 x = 14 by 2:
(2 x)/2 = 14/2

2/2 = 1:
x = 14/2

The gcd of 14 and 2 is 2, so 14/2 = (2×7)/(2×1) = 2/2×7 = 7:
Answer:  x = 7

____________________________________________________________

2.)  Solve for x:
3 x - 2 (5 - x) = 3 x - 3 (x - 10)

-2 (5 - x) = 2 x - 10:
2 x - 10 + 3 x = 3 x - 3 (x - 10)

Grouping like terms, 3 x + 2 x - 10 = (3 x + 2 x) - 10:
(3 x + 2 x) - 10 = 3 x - 3 (x - 10)

3 x + 2 x = 5 x:
5 x - 10 = 3 x - 3 (x - 10)

-3 (x - 10) = 30 - 3 x:
5 x - 10 = 30 - 3 x + 3 x

3 x - 3 x = 0:
5 x - 10 = 30

Add 10 to both sides:
5 x + (10 - 10) = 10 + 30

10 - 10 = 0:
5 x = 30 + 10

30 + 10 = 40:
5 x = 40

Divide both sides of 5 x = 40 by 5:
(5 x)/5 = 40/5

5/5 = 1:
x = 40/5

The gcd of 40 and 5 is 5, so 40/5 = (5×8)/(5×1) = 5/5×8 = 8:

<span>Answer: x = 8

_________________________________________________________

3.) Solve for x:</span>
5 (x + 1) = 3 (2 x + 3) + 5

3 (2 x + 3) = 6 x + 9:
5 (x + 1) = 6 x + 9 + 5

Grouping like terms, 6 x + 5 + 9 = 6 x + (9 + 5):
5 (x + 1) = 6 x + (9 + 5)

9 + 5 = 14:
5 (x + 1) = 6 x + 14

Expand out terms of the left hand side:
5 x + 5 = 6 x + 14

Subtract 6 x from both sides:
(5 x - 6 x) + 5 = (6 x - 6 x) + 14

5 x - 6 x = -x:
-x + 5 = (6 x - 6 x) + 14

6 x - 6 x = 0:
5 - x = 14

Subtract 5 from both sides:
(5 - 5) - x = 14 - 5

5 - 5 = 0:
-x = 14 - 5

14 - 5 = 9:
-x = 9

Multiply both sides of -x = 9 by -1:
(-x)/(-1) = -9
(-1)/(-1) = 1:

<span>Answer: x = -9</span>
You might be interested in
Crafter's Warehouse sells 3 yards of gray tulle for $5.63. They sell 6 feet of black tulle for $3.58. Which tulle has the better
Sindrei [870]

Answer:

The black tulle is the better buy

Step-by-step explanation:

You will need to find the unit rate for the tulle...in other words cost per 1 yard to see which is the better buy.

You also need to make sure they are in the same units. So, we will convert the 3 yards to feet....which will be 9 feet

5.63/9 = 0.62555 per foot

3.58/6 = 0.59666 per foot

3 0
3 years ago
Rodger is riding in a bike-a-thon to raise money for his favorite charity. The total distance of the bike of stone is 38.7 miles
Len [333]
Did u mean miles? cause it says "mouse"

8 0
3 years ago
Read 2 more answers
B 5 3 a 4 What is the length of the hypotenuse of this triangle? 3 units 5 units 4 units​
Lunna [17]

Answer:

5 units

Step-by-step explanation:

The hypotenuse is always the longest segment on a triangle. If the lengths of the sides of this triangle are 3 units, 4 units, and 5 units, the hypotenuse will be 5 units. You can use the pythagorean theorem to check.

a^2+b^2=c^2

If you substitute the variable with the lengths of the legs in ascending order, you will get 3^2+4^2=5^2. Simplifying the equation, you will get 9+16=25, or 25=25. Thus, proving the equation.

Hope this helped! :)

6 0
3 years ago
CALCULUS: Determine which function is a solution to the differential equation y ' − y = 0.
Montano1993 [528]

C: none of these are solutions to the given equation.

• If<em> y(x)</em> = <em>e</em>², then <em>y</em> is constant and <em>y'</em> = 0. Then <em>y'</em> - <em>y</em> = -<em>e</em>² ≠ 0.

• If <em>y(x)</em> = <em>x</em>, then <em>y'</em> = 1, but <em>y'</em> - <em>y</em> = 1 - <em>x</em> ≠ 0.

The actual solution is easy to find, since this equation is separable.

<em>y'</em> - <em>y</em> = 0

d<em>y</em>/d<em>x</em> = <em>y</em>

d<em>y</em>/<em>y</em> = d<em>x</em>

∫ d<em>y</em>/<em>y</em> = ∫ d<em>x</em>

ln|<em>y</em>| = <em>x</em> + <em>C</em>

<em>y</em> = exp(<em>x</em> + <em>C </em>)

<em>y</em> = <em>C</em> exp(<em>x</em>) = <em>C</em> <em>eˣ</em>

8 0
2 years ago
Last year, 45% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indica
natka813 [3]

Answer:

a)x₁  = 24  business owners plan to provide a gift this year

b)  p-value = 0,0017

c)p-value < α   we have to eject H₀   And support the claim that the proportion of business owners providing gifts has decrease

Step-by-step explanation:

a) Sample size 80

proportion  p₁  = 30 %   p₁ = 0,3

Then   x₁ = 80*0,3

x₁  = 24  business owners plan to provide a gift this year

b) Hypothesis Test

Null Hypothesis                    H₀          p₁  =  0,45

Alternative Hypothesis        Hₐ          p₁  <  0,45

p₁  =  0,3   then  q₁  =  1  -  0,3    q₁ =  0,7

z(s)  = ( p₁  -  0,45 )/ √p₁* q₁ / n

z(s)  =  -  0,15 / √0,002625

z(s) = - 0,15 / 0,05123

z(s) = - 2,9279

b)From z-table we find  p-value = 0,0017

c) If  α = 0,05   ( significance level )  as

p-value < α   we have to eject H₀   And support the claim that the proportion of business owners providing gifts has decrease

6 0
2 years ago
Other questions:
  • Anyone feel like helping? lol
    12·1 answer
  • 6 1/2 times 1 3/5 in fraction form
    11·2 answers
  • Franklin picked 342 potatoes out of his garden this season and will store them in 6 baskets.
    9·1 answer
  • Can you plz help me with this math problem?
    8·2 answers
  • 876 divided by 43 plz help
    8·1 answer
  • Need answers to three questions in picture will give brainly
    6·2 answers
  • Sarah will take 8 algebra tests. On the first 7, Sarah's scores were 79, 86, 92, 89, 87, 80, and 82. What will Sarah need to sco
    6·1 answer
  • Gail, Lucas, and Joel are playing a number game where they must draw a card with a number on it. Then they compare the numbers o
    12·2 answers
  • I just need it solve thats all
    10·1 answer
  • A group of 15 people are going to run a race. The top 8 will advance to the finals. Determine if the situation is a permutation
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!