Solved on Sep 27, 2023

Solve the equation $-2(8-7x)-(1-x)=2(x-5)$ and check your answer.

STEP 1

Assumptions1. The equation given is $-(8-7x)-(1-x)=(x-5)$ . We need to find the value of $x$ that satisfies the equation

STEP 2

First, we will simplify the equation by distributing the multiplication across the terms in the parentheses.
$-2(8-7x)-(1-x)=2(x-5)$ becomes $-16+14x-(1-x)=2x-10$

STEP 3

Next, we simplify the equation by combining like terms on both sides.
$-16+14x-1+x=2x-10$ becomes $-17+15x=2x-10$

STEP 4

Now, we will isolate the variable $x$ on one side of the equation. We can do this by subtracting $2x$ from both sides of the equation.
$-17+15x-2x=2x-10-2x$ which simplifies to $-17+13x=-10$

STEP 5

Next, we will isolate $x$ by adding $17$ to both sides of the equation.
$-17+13x+17=-10+17$ which simplifies to $13x=7$

STEP 6

Finally, we solve for $x$ by dividing both sides of the equation by $13$ .
$x=\frac{}{13}$

STEP 7

Now, we will check our answer by substituting $x=\frac{7}{13}$ back into the original equation.
$-2(-7(\frac{7}{13}))-(1-\frac{7}{13})=2((\frac{7}{13})-5)$

STEP 8

implify the equation by performing the operations.
$-2(8-\frac{49}{13})-(\frac{6}{13})=2(\frac{7}{13}-5)$ becomes $-2(\frac{55}{13})-(\frac{6}{13})=2(\frac{-58}{13})$

STEP 9

implify the equation further.
$-\frac{110}{13}-\frac{6}{13}=-\frac{116}{13}$ becomes $-\frac{116}{13}=-\frac{116}{13}$ Since the left-hand side equals the right-hand side, our solution is correct.
The solution to the equation is $x=\frac{7}{13}$ .

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Solve the equation $-2(8-7x)-(1-x)=2(x-5)$ and check your answer.

STEP 1

Assumptions1. The equation given is $-(8-7x)-(1-x)=(x-5)$ . We need to find the value of $x$ that satisfies the equation

STEP 2

First, we will simplify the equation by distributing the multiplication across the terms in the parentheses.
$-2(8-7x)-(1-x)=2(x-5)$ becomes $-16+14x-(1-x)=2x-10$

STEP 3

Next, we simplify the equation by combining like terms on both sides.
$-16+14x-1+x=2x-10$ becomes $-17+15x=2x-10$

STEP 4

Now, we will isolate the variable $x$ on one side of the equation. We can do this by subtracting $2x$ from both sides of the equation.
$-17+15x-2x=2x-10-2x$ which simplifies to $-17+13x=-10$

STEP 5

Next, we will isolate $x$ by adding $17$ to both sides of the equation.
$-17+13x+17=-10+17$ which simplifies to $13x=7$

STEP 6

Finally, we solve for $x$ by dividing both sides of the equation by $13$ .
$x=\frac{}{13}$

STEP 7

Now, we will check our answer by substituting $x=\frac{7}{13}$ back into the original equation.
$-2(-7(\frac{7}{13}))-(1-\frac{7}{13})=2((\frac{7}{13})-5)$

STEP 8

implify the equation by performing the operations.
$-2(8-\frac{49}{13})-(\frac{6}{13})=2(\frac{7}{13}-5)$ becomes $-2(\frac{55}{13})-(\frac{6}{13})=2(\frac{-58}{13})$

STEP 9

implify the equation further.
$-\frac{110}{13}-\frac{6}{13}=-\frac{116}{13}$ becomes $-\frac{116}{13}=-\frac{116}{13}$ Since the left-hand side equals the right-hand side, our solution is correct.
The solution to the equation is $x=\frac{7}{13}$ .

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Solve the equation −2(8−7x)−(1−x)=2(x−5)-2(8-7x)-(1-x)=2(x-5)−2(8−7x)−(1−x)=2(x−5) and check your answer.

STEP 1

Assumptions1. The equation given is −(8−7x)−(1−x)=(x−5)-(8-7x)-(1-x)=(x-5)−(8−7x)−(1−x)=(x−5). We need to find the value of xxx that satisfies the equation

STEP 2

First, we will simplify the equation by distributing the multiplication across the terms in the parentheses.−2(8−7x)−(1−x)=2(x−5)-2(8-7x)-(1-x)=2(x-5)−2(8−7x)−(1−x)=2(x−5)becomes−16+14x−(1−x)=2x−10-16+14x-(1-x)=2x-10−16+14x−(1−x)=2x−10

STEP 3

Next, we simplify the equation by combining like terms on both sides.−16+14x−1+x=2x−10-16+14x-1+x=2x-10−16+14x−1+x=2x−10becomes−17+15x=2x−10-17+15x=2x-10−17+15x=2x−10

STEP 4

Now, we will isolate the variable xxx on one side of the equation. We can do this by subtracting 2x2x2x from both sides of the equation.−17+15x−2x=2x−10−2x-17+15x-2x=2x-10-2x−17+15x−2x=2x−10−2xwhich simplifies to−17+13x=−10-17+13x=-10−17+13x=−10

STEP 5

Next, we will isolate xxx by adding 171717 to both sides of the equation.−17+13x+17=−10+17-17+13x+17=-10+17−17+13x+17=−10+17which simplifies to13x=713x=713x=7

STEP 6

Finally, we solve for xxx by dividing both sides of the equation by 131313.x=13x=\frac{}{13}x=13​

STEP 7

Now, we will check our answer by substituting x=713x=\frac{7}{13}x=137​ back into the original equation.−2(−7(713))−(1−713)=2((713)−5)-2(-7(\frac{7}{13}))-(1-\frac{7}{13})=2((\frac{7}{13})-5)−2(−7(137​))−(1−137​)=2((137​)−5)

STEP 8

STEP 9

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Solve the equation $-2(8-7x)-(1-x)=2(x-5)$ and check your answer.

Assumptions1. The equation given is $-(8-7x)-(1-x)=(x-5)$ . We need to find the value of $x$ that satisfies the equation

First, we will simplify the equation by distributing the multiplication across the terms in the parentheses.
$-2(8-7x)-(1-x)=2(x-5)$ becomes $-16+14x-(1-x)=2x-10$

Next, we simplify the equation by combining like terms on both sides.
$-16+14x-1+x=2x-10$ becomes $-17+15x=2x-10$

Now, we will isolate the variable $x$ on one side of the equation. We can do this by subtracting $2x$ from both sides of the equation.
$-17+15x-2x=2x-10-2x$ which simplifies to $-17+13x=-10$

Next, we will isolate $x$ by adding $17$ to both sides of the equation.
$-17+13x+17=-10+17$ which simplifies to $13x=7$

Finally, we solve for $x$ by dividing both sides of the equation by $13$ .
$x=\frac{}{13}$

Now, we will check our answer by substituting $x=\frac{7}{13}$ back into the original equation.
$-2(-7(\frac{7}{13}))-(1-\frac{7}{13})=2((\frac{7}{13})-5)$