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3 years ago

Given the equation 4x − 26 = 2x − 4, which order of operations completely solves for x?

1 answer:

6 0

4x - 26 = 2x - 4....subtract 2x from both sides
4x - 2x - 26 = -4...add 26 to both sides
4x - 2x = -4 + 26...combine terms
2x = 22...divide both sides by 2
x = 22/2 = 11

OR
4x - 26 = 2x - 4.....subtract 4x from both sides
-26 = 2x - 4x - 4....add 4 to both sides
-26 + 4 = 2x - 4x...combine terms
-22 = -2x....divide both sides by -2
-22/-2 = x
11 = x

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sveta [45]

This question was not written properly

Complete Question

Steve has 54 stamps in his collection of 13 cent, 29 cent, and 45 cent stamps, totaling a value of $15.98. If the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80. Find the number of each type of stamp in his collection.

Answer:

a) The number of 13 cent = 14

b) The number of 29 cent = 24

c) The number of 45 cent = 16

Step-by-step explanation:

We are told he has 54 stamps in total.

These stamps are;13 cent, 29 cent, and 45 cent stamps.

Let's

Number of 13 cent = a

Number of 29 cent = b

Number of 45 cent = c

Hence,

a + b + c = 54........... Equation 1

The total value of the 3 stamps are $15.98.

1 cent = $0.01

We have

0.13a + 0.29b + 0.45c= $15.98 ......... Equation 2

We know from the question that:

13 cent stamps is doubled, the new total value of his stamp collection would be $17.80.

Therefore

2(0.13a) + 0.29b + 0.45c = 17.8

0.26a + 0.29b + 0.45c = 17.8 ......... Equation 3

Combining Equation 2 and 3 together

0.13a + 0.29b + 0.45c= 15.98 ......... Equation 2

0.26a + 0.29b + 0.45c = 17.8 ......... Equation 3

We eliminate b and c by Subtracting Equation 3 from 3

0.13a = 1.82

a = 1.82/0.13

a = 14

a + b + c = 54........... Equation 1

Since a = 14

14 + b + c = 54

b + c = 54 - 14

b + c = 40

c = 40 - b

Substitute 40 - b for c and 14 for a is Equation 2

0.13a + 0.29b + 0.45c= 15.98 ......... Equation 2

0.13(14 ) + 0.29b + 0.45(40 - b) = 15.98

= 1.82 + 0.29b + 18 - 0.45b = 15.98

Collect like terms

1.82 + 18 - 15.98 = 0.45b - 0.29b

3.84 = 0.16b

b = 3.84/0.16

b = 24

Hence: Solving for c

a + b + c = 54........... Equation 1

14 + 24 + c = 54

38 + c = 54

c = 54 - 38

c = 16

Therefore,

The number of 13 cent = 14

The number of 29 cent = 24

The number of 45 cent = 16

8 0

3 years ago

Boden's account has a principal of $400 and a simple interest rate of 3.6%. Complete the number line. How much money will be i

Tju [1.3M]

400x1.036 then that multiplied by 1.036 and every answer just multiply by that

8 0

3 years ago

Read 2 more answers

-x-5y=22&y=-7x+16 solve the system by the substitution method

Kaylis [27]

(3,-5) is your answer .-.

4 0

3 years ago

Please can someone help me with this question

sasho [114]

Answer:

r = - $\frac{6a}{1-5m^2}$

Step-by-step explanation:

Rewrite the equation as $\sqrt{x} 6a+r/5r$ = m

Remove the radical on the left side of the equation by squaring both sides of the equation.

( $\sqrt{\frac{6a+r}{5r} )^{2}$ = m^2

Then, you simplify each of the equation.

Rewrite: ( $\sqrt{\frac{6a+r}{5r} )^{2}$ as $\frac{6a+r}{5r} = m^{2}$

Remove any parentheses if needed.

Solve for r.

Multiply each term by r and simplify."

Multiply both sides of the equation by 5.

6a+r= m^2r⋅(5)

Remove parentheses.

Move 5 to the left of (m ^2) r

6a+r=5m^2)r

Subtract 5m^2)r from both sides of the equation.

6a+r-5m^2)r=0

Subtract 6a from both sides of the equation.

r-5m^2)r=-6a

Factor r out of r-5m^2)r

r(1-5m^2)=-6a

Divide each term by 1-5m^2 and simplify.

r = - $\frac{6a}{1-5m^2}$

There you go, hope this helps!

4 0

3 years ago

Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball

Ede4ka [16]

If Jim has x football cards He will have 5x baseballs cards Thus x + 5x = 120 > total # of cards 6x = 120 x= 120/6 = 20 so Jim has 5x baseball cards = 20*5 =100 baseball cards

6 0

3 years ago