Math / Algebra

Question竑 ${ }^{-1}$ Find the missing number so that the equation has no solutions. $\square$ $x+18=-5 x-11$ Submit

Studdy Solution

STEP 1

1. The equation is linear in terms of $x$ .
2. We are looking for a value that makes the equation have no solutions.
3. An equation has no solutions if it results in a contradiction, such as a false statement like $0 = c$ where $c$ is a non-zero constant.

STEP 2

1. Simplify the equation.
2. Rearrange terms to isolate $x$ .
3. Determine the condition for no solutions.
4. Solve for the missing number.

STEP 3

Start by simplifying the given equation:
$\square x + 18 = -5x - 11$

STEP 4

Rearrange the terms to isolate $x$ on one side. Move all terms involving $x$ to one side and constant terms to the other side:
$\square x + 5x = -11 - 18$
Combine like terms:
$(\square + 5)x = -29$

STEP 5

For the equation to have no solutions, the coefficient of $x$ must be zero, leading to a contradiction. This means:
$\square + 5 = 0$

STEP 6

Solve for the missing number:
$\square + 5 = 0$ $\square = -5$
The missing number is $\boxed{-5}$ .

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Question竑 ${ }^{-1}$ Find the missing number so that the equation has no solutions. $\square$ $x+18=-5 x-11$ Submit

Studdy Solution

STEP 1

1. The equation is linear in terms of $x$ .
2. We are looking for a value that makes the equation have no solutions.
3. An equation has no solutions if it results in a contradiction, such as a false statement like $0 = c$ where $c$ is a non-zero constant.

STEP 2

1. Simplify the equation.
2. Rearrange terms to isolate $x$ .
3. Determine the condition for no solutions.
4. Solve for the missing number.

STEP 3

Start by simplifying the given equation:
$\square x + 18 = -5x - 11$

STEP 4

Rearrange the terms to isolate $x$ on one side. Move all terms involving $x$ to one side and constant terms to the other side:
$\square x + 5x = -11 - 18$
Combine like terms:
$(\square + 5)x = -29$

STEP 5

For the equation to have no solutions, the coefficient of $x$ must be zero, leading to a contradiction. This means:
$\square + 5 = 0$

STEP 6

Solve for the missing number:
$\square + 5 = 0$ $\square = -5$
The missing number is $\boxed{-5}$ .

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Question竑 −1{ }^{-1}−1 Find the missing number so that the equation has no solutions. □\square□ x+18=−5x−11x+18=-5 x-11x+18=−5x−11 Submit

Studdy Solution

STEP 1

1. The equation is linear in terms of x x x.2. We are looking for a value that makes the equation have no solutions.3. An equation has no solutions if it results in a contradiction, such as a false statement like 0=c 0 = c 0=c where c c c is a non-zero constant.

STEP 2

1. Simplify the equation.2. Rearrange terms to isolate x x x.3. Determine the condition for no solutions.4. Solve for the missing number.

STEP 3

Start by simplifying the given equation:□x+18=−5x−11 \square x + 18 = -5x - 11 □x+18=−5x−11

STEP 4

Rearrange the terms to isolate x x x on one side. Move all terms involving x x x to one side and constant terms to the other side:□x+5x=−11−18 \square x + 5x = -11 - 18 □x+5x=−11−18Combine like terms:(□+5)x=−29 (\square + 5)x = -29 (□+5)x=−29

STEP 5

For the equation to have no solutions, the coefficient of x x x must be zero, leading to a contradiction. This means:□+5=0 \square + 5 = 0 □+5=0

STEP 6

Solve for the missing number:□+5=0 \square + 5 = 0 □+5=0 □=−5 \square = -5 □=−5 The missing number is −5 \boxed{-5} −5​.

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Question竑 ${ }^{-1}$ Find the missing number so that the equation has no solutions. $\square$ $x+18=-5 x-11$ Submit

1. The equation is linear in terms of $x$ .
2. We are looking for a value that makes the equation have no solutions.
3. An equation has no solutions if it results in a contradiction, such as a false statement like $0 = c$ where $c$ is a non-zero constant.

1. Simplify the equation.
2. Rearrange terms to isolate $x$ .
3. Determine the condition for no solutions.
4. Solve for the missing number.

Start by simplifying the given equation:
$\square x + 18 = -5x - 11$

Rearrange the terms to isolate $x$ on one side. Move all terms involving $x$ to one side and constant terms to the other side:
$\square x + 5x = -11 - 18$
Combine like terms:
$(\square + 5)x = -29$

For the equation to have no solutions, the coefficient of $x$ must be zero, leading to a contradiction. This means:
$\square + 5 = 0$

Solve for the missing number:
$\square + 5 = 0$ $\square = -5$
The missing number is $\boxed{-5}$ .