QuestionSolve the equation $2(8x - 1) = 25$ and verify your solution by substituting it back into the original equation.

Studdy Solution

STEP 1

Assumptions1. The equation to solve is $(8x-1)=25$ . . We are solving for the variable $x$ .

STEP 2

First, we need to distribute the $2$ on the left side of the equation. We do this by multiplying $2$ by each term inside the parentheses.
$2(8x-1) =28x -21$

STEP 3

After distributing, the equation becomes $16x -2 =25$

STEP 4

Next, we need to isolate the term with the variable $x$ on one side of the equation. We do this by adding $2$ to both sides of the equation.
$16x -2 +2 =25 +2$

STEP 5

After adding, the equation becomes $16x =27$

STEP 6

Finally, we solve for $x$ by dividing both sides of the equation by $16$ .
$x = \frac{27}{16}$

STEP 7

Now, we need to check our proposed solution by substituting it for the variable $x$ in the original equation.
$2(*\frac{27}{16}-1)$

STEP 8

implify the equation by performing the multiplication first (according to the order of operations, BIDMAS/BODMAS/PEDMAS).
$2(\frac{216}{16}-1)$

STEP 9

Further simplify the equation by performing the subtraction.
$2(\frac{200}{16})$

STEP 10

Finally, perform the multiplication.
$\frac{400}{16}$

STEP 11

implify to get the final result.
$25$ Since the result matches the right side of the original equation, our solution is correct.
The solution to the equation $(8x-)=25$ is $x=\frac{27}{16}$ .

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QuestionSolve the equation $2(8x - 1) = 25$ and verify your solution by substituting it back into the original equation.

Studdy Solution

STEP 1

Assumptions1. The equation to solve is $(8x-1)=25$ . . We are solving for the variable $x$ .

STEP 2

First, we need to distribute the $2$ on the left side of the equation. We do this by multiplying $2$ by each term inside the parentheses.
$2(8x-1) =28x -21$

STEP 3

After distributing, the equation becomes $16x -2 =25$

STEP 4

Next, we need to isolate the term with the variable $x$ on one side of the equation. We do this by adding $2$ to both sides of the equation.
$16x -2 +2 =25 +2$

STEP 5

After adding, the equation becomes $16x =27$

STEP 6

Finally, we solve for $x$ by dividing both sides of the equation by $16$ .
$x = \frac{27}{16}$

STEP 7

Now, we need to check our proposed solution by substituting it for the variable $x$ in the original equation.
$2(*\frac{27}{16}-1)$

STEP 8

implify the equation by performing the multiplication first (according to the order of operations, BIDMAS/BODMAS/PEDMAS).
$2(\frac{216}{16}-1)$

STEP 9

Further simplify the equation by performing the subtraction.
$2(\frac{200}{16})$

STEP 10

Finally, perform the multiplication.
$\frac{400}{16}$

STEP 11

implify to get the final result.
$25$ Since the result matches the right side of the original equation, our solution is correct.
The solution to the equation $(8x-)=25$ is $x=\frac{27}{16}$ .

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QuestionSolve the equation 2(8x−1)=252(8x - 1) = 252(8x−1)=25 and verify your solution by substituting it back into the original equation.

Studdy Solution

STEP 1

Assumptions1. The equation to solve is (8x−1)=25(8x-1)=25(8x−1)=25. . We are solving for the variable xxx.

STEP 2

First, we need to distribute the 222 on the left side of the equation. We do this by multiplying 222 by each term inside the parentheses.2(8x−1)=2∗8x−2∗12(8x-1) =2*8x -2*12(8x−1)=2∗8x−2∗1

STEP 3

After distributing, the equation becomes16x−2=2516x -2 =2516x−2=25

STEP 4

Next, we need to isolate the term with the variable xxx on one side of the equation. We do this by adding 222 to both sides of the equation.16x−2+2=25+216x -2 +2 =25 +216x−2+2=25+2

STEP 5

After adding, the equation becomes16x=2716x =2716x=27

STEP 6

Finally, we solve for xxx by dividing both sides of the equation by 161616.x=2716x = \frac{27}{16}x=1627​

STEP 7

Now, we need to check our proposed solution by substituting it for the variable xxx in the original equation.2(∗2716−1)2(*\frac{27}{16}-1)2(∗1627​−1)

STEP 8

implify the equation by performing the multiplication first (according to the order of operations, BIDMAS/BODMAS/PEDMAS).2(21616−1)2(\frac{216}{16}-1)2(16216​−1)

STEP 9

Further simplify the equation by performing the subtraction.2(20016)2(\frac{200}{16})2(16200​)

STEP 10

Finally, perform the multiplication.40016\frac{400}{16}16400​

STEP 11

implify to get the final result.252525Since the result matches the right side of the original equation, our solution is correct.The solution to the equation (8x−)=25(8x-)=25(8x−)=25 is x=2716x=\frac{27}{16}x=1627​.

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QuestionSolve the equation $2(8x - 1) = 25$ and verify your solution by substituting it back into the original equation.

Assumptions1. The equation to solve is $(8x-1)=25$ . . We are solving for the variable $x$ .

First, we need to distribute the $2$ on the left side of the equation. We do this by multiplying $2$ by each term inside the parentheses.
$2(8x-1) =28x -21$

After distributing, the equation becomes $16x -2 =25$

Next, we need to isolate the term with the variable $x$ on one side of the equation. We do this by adding $2$ to both sides of the equation.
$16x -2 +2 =25 +2$

After adding, the equation becomes $16x =27$

Finally, we solve for $x$ by dividing both sides of the equation by $16$ .
$x = \frac{27}{16}$

Now, we need to check our proposed solution by substituting it for the variable $x$ in the original equation.
$2(*\frac{27}{16}-1)$

implify the equation by performing the multiplication first (according to the order of operations, BIDMAS/BODMAS/PEDMAS).
$2(\frac{216}{16}-1)$

Further simplify the equation by performing the subtraction.
$2(\frac{200}{16})$

Finally, perform the multiplication.
$\frac{400}{16}$

implify to get the final result.
$25$ Since the result matches the right side of the original equation, our solution is correct.
The solution to the equation $(8x-)=25$ is $x=\frac{27}{16}$ .