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jonny [76]
2 years ago
12

13. (07.05 MC) What is the solution to the equation 5x + 2(x - 4) = 5x + x - 10? (1 point) O​

Mathematics
1 answer:
TEA [102]2 years ago
7 0

Answer:

x = -2

Step-by-step explanation:

5x + 2(x - 4) = 5x + x - 10

First, we need to to multiply out the parathesis in the equation:

5x + 2(x - 4) = 5x + x - 10

5x + 2x - 8 = 5x + x - 10

Next, we can combine "like terms" to simplify the equation further:

5x + 2x - 8 = 5x + x - 10

7x - 8 = 6x - 10

Now we can isolate the variable "x" to one side:

7x - 8 = 6x - 10

x - 8 = -10

x = -2

To check our work, we can replace x with -2 in our original equation:

5x + 2(x - 4) = 5x + x - 10

5(-2) + 2 (-2 - 4) = 5(-2) + -2 - 10

-10 + 2 (-6) = -10 -2 - 10

-22 = -22

I hope this helps!

-TheBusinessMan

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Answer:

Multiply the top equation by -3 and the bottom equation by 2

Step-by-step explanation:

Given <u>system of equations</u>:

\begin{cases}4x-2y=7\\3x-3y=15 \end{cases}

To solve the given system of equations by addition, make one of the variables in both equations <u>sum to zero</u>.  To do this, the chosen variable must have the <u>same coefficient</u>, but it should be <u>negative</u> in one equation and <u>positive</u> in the other, so that when the two equations are added together, the variable is <u>eliminated</u>.

<u>To eliminate the </u><u>variable y</u>:

Multiply the top equation by -3 to make the coefficient of the y variable 6:

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Multiply the bottom equation by 2 to make the coefficient of the y variable -6:

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Add the two equations together to <u>eliminate y</u>:

\begin{array}{l r r}& -12x+6y= &-21\\+ & 6x-6y= & 30\\\cline{1-3}& -6x\phantom{))))))} = & 9\end{array}

<u>Solve</u> for x:

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<u>Substitute</u> the found value of x into one of the equations and <u>solve for y</u>:

\implies 3\left(-\dfrac{3}{2}\right)-3y=15

\implies -\dfrac{9}{2}-3y=15

\implies -3y=\dfrac{39}{2}

\implies y=-\dfrac{39}{2 \cdot 3}

\implies y=-\dfrac{13}{2}

Learn more about systems of equations here:

brainly.com/question/27868564

brainly.com/question/27520807

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