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meriva
3 years ago
14

Rewrite 48 + 60 using the distributive property

Mathematics
1 answer:
Flauer [41]3 years ago
3 0

Answer:

12* ( 4+5)

Step-by-step explanation:

48 = 12 * 4

60 = 12 * 5

48 + 60 = 12*4 + 12*5

             = 12*( 4 + 5)

            = 12* 9

            = 108

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Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all tha
vodomira [7]

we have

\frac{3}{5}x+ \frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x

Combine like terms in both sides

(\frac{3}{5}x+ x)+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x

we know that

(\frac{3}{5}x+ x)=(\frac{3}{5}x+ \frac{5}{5}x)=\frac{8}{5}x

substitute in the expression above

\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x-----> equation A        

Multiply equation A by 5*3*2=30 both sides

30*(\frac{8}{5}x+\frac{2}{3})=30*(\frac{1}{2}-\frac{1}{5}x)

48x+20=15-6x ---------> equation B

Group terms that contain the same variable, and move the constant to the opposite side of the equation

48x+6x=15-20

54x=-5 ---------> equation C

Solve for x

x=-\frac{5}{54} =-0.09

We are going to proceed to verify each case to determine the solution.

<u>Case a)</u> \frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x

the case a) is equal to the equation A

so

the case a) have the same solution that the given equation

<u>Case b)</u> 18x+20+30x=15-6x

Combine like terms in left side

(18x+30x)+20=15-6x

(48x)+20=15-6x

the case b) is equal to the equation B

so

the case b) have the same solution that the given equation

<u>Case c)</u> 18x+20+x=15-6x

Combine like terms in left side

(18x+x)+20=15-6x

(19x)+20=15-6x

19x+6x=15-20\\25x=-5\\x=-0.20

-0.20\neq -0.09

therefore

the case c) not have the same solution that the given equation

<u>Case d)</u> 24x+30x=-5

Combine like terms in left side

54x=-5

the case d) is equal to the equation C

so

the case d) have the same solution that the given equation

<u>Case e)</u> 12x+30x=-5

Combine like terms in left side

42x=-5

x=-5/42=-0.12

-0.12\neq -0.09

therefore

the case e) not have the same solution that the given equation

therefore

<u>the answer is</u>

case a) \frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x

case b) 18x+20+30x=15-6x

case d) 24x+30x=-5

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It should take like 3 hours so D.

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