Which graph shows the solution set of

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.

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

the case a) is equal to the equation A

so

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

Case b) $18x+20+30x=15-6x$

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

Case c) $18x+20+x=15-6x$

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

Case d) $24x+30x=-5$

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

Case e) $12x+30x=-5$

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

the answer is

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) $24x+30x=-5$

7 0

4 years ago

Read 2 more answers

A year membership to Fun Zone costs $45 plus $1 per visit. A one-month membership costs $5 plus $3 per visit. Which multi-step e

Margaret [11]

Answer:

y = $45 + x

y = $5 + 3x

Step-by-step explanation:

The computation of the multi-step equations be shown below:

Let us assume the number of visits be x

So the first equation would be

y = $45 + x

And, the second equation would be

y = $5 + 3x

These are the multi-step equations with variable on the both sides

6 0

3 years ago

Number 6 please help me

swat32

I am pretty sure it is 39 but I am not exactly sure. You might want someone else to solve this too. I did 27*.45=12.15 then I did 12.15+27=39.15 then I rounded the answer to the nearest whole number.

I hope this helped you:)

3 0

3 years ago

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Find the values of these fractions:

VladimirAG [237]

I would say answer 1 honestly good luck

3 0

3 years ago

Solve for y 2y - 11 > -19.

Talja [164]

Answer:

Y>-4

Step-by-step explanation:

Add 11 to both sides and divide

3 0

4 years ago

Read 2 more answers