Solved on Dec 01, 2023

Find the number of solutions to the linear equation $-6-h=-h+4-2h$ .

STEP 1

Assumptions
1. The equation given is $-6-h=-h+4-2h$

STEP 2

First, we should simplify the equation by combining like terms on both sides. On the right side of the equation, we can combine the $-h$ and $-2h$ terms.
$-6-h=-3h+4$

STEP 3

Next, we can isolate the variable $h$ on one side of the equation. To do this, we can add $3h$ to both sides of the equation to cancel out the $-3h$ on the right side.
$-6-h+3h=4$

STEP 4

Simplify the left side of the equation by combining the $-h$ and $3h$ terms.
$-6+2h=4$

STEP 5

Next, we can isolate the variable $h$ on one side of the equation. To do this, we can add $6$ to both sides of the equation to cancel out the $-6$ on the left side.
$2h=4+6$

STEP 6

Simplify the right side of the equation by adding $4$ and $6$ .
$2h=10$

STEP 7

Finally, we can solve for $h$ by dividing both sides of the equation by $2$ .
$h=10/2$

STEP 8

Calculate the value of $h$ .
$h=5$
The equation has one solution, $h=5$ .

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Find the number of solutions to the linear equation $-6-h=-h+4-2h$ .

STEP 1

Assumptions
1. The equation given is $-6-h=-h+4-2h$

STEP 2

First, we should simplify the equation by combining like terms on both sides. On the right side of the equation, we can combine the $-h$ and $-2h$ terms.
$-6-h=-3h+4$

STEP 3

Next, we can isolate the variable $h$ on one side of the equation. To do this, we can add $3h$ to both sides of the equation to cancel out the $-3h$ on the right side.
$-6-h+3h=4$

STEP 4

Simplify the left side of the equation by combining the $-h$ and $3h$ terms.
$-6+2h=4$

STEP 5

Next, we can isolate the variable $h$ on one side of the equation. To do this, we can add $6$ to both sides of the equation to cancel out the $-6$ on the left side.
$2h=4+6$

STEP 6

Simplify the right side of the equation by adding $4$ and $6$ .
$2h=10$

STEP 7

Finally, we can solve for $h$ by dividing both sides of the equation by $2$ .
$h=10/2$

STEP 8

Calculate the value of $h$ .
$h=5$
The equation has one solution, $h=5$ .

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Find the number of solutions to the linear equation −6−h=−h+4−2h-6-h=-h+4-2h−6−h=−h+4−2h.

STEP 1

Assumptions1. The equation given is −6−h=−h+4−2h-6-h=-h+4-2h−6−h=−h+4−2h

STEP 2

First, we should simplify the equation by combining like terms on both sides. On the right side of the equation, we can combine the −h-h−h and −2h-2h−2h terms.−6−h=−3h+4-6-h=-3h+4−6−h=−3h+4

STEP 3

Next, we can isolate the variable hhh on one side of the equation. To do this, we can add 3h3h3h to both sides of the equation to cancel out the −3h-3h−3h on the right side.−6−h+3h=4-6-h+3h=4−6−h+3h=4

STEP 4

Simplify the left side of the equation by combining the −h-h−h and 3h3h3h terms.−6+2h=4-6+2h=4−6+2h=4

STEP 5

Next, we can isolate the variable hhh on one side of the equation. To do this, we can add 666 to both sides of the equation to cancel out the −6-6−6 on the left side.2h=4+62h=4+62h=4+6

STEP 6

Simplify the right side of the equation by adding 444 and 666.2h=102h=102h=10

STEP 7

Finally, we can solve for hhh by dividing both sides of the equation by 222.h=10/2h=10/2h=10/2

STEP 8

Calculate the value of hhh.h=5h=5h=5The equation has one solution, h=5h=5h=5.

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Find the number of solutions to the linear equation $-6-h=-h+4-2h$ .

Assumptions
1. The equation given is $-6-h=-h+4-2h$

First, we should simplify the equation by combining like terms on both sides. On the right side of the equation, we can combine the $-h$ and $-2h$ terms.
$-6-h=-3h+4$

Next, we can isolate the variable $h$ on one side of the equation. To do this, we can add $3h$ to both sides of the equation to cancel out the $-3h$ on the right side.
$-6-h+3h=4$

Simplify the left side of the equation by combining the $-h$ and $3h$ terms.
$-6+2h=4$

Next, we can isolate the variable $h$ on one side of the equation. To do this, we can add $6$ to both sides of the equation to cancel out the $-6$ on the left side.
$2h=4+6$

Simplify the right side of the equation by adding $4$ and $6$ .
$2h=10$

Finally, we can solve for $h$ by dividing both sides of the equation by $2$ .
$h=10/2$

Calculate the value of $h$ .
$h=5$
The equation has one solution, $h=5$ .