QuestionWhat equation(s) have no solutions? Select ALL that apply. $5 x-5=x$ $3(x+4)=3 x+10$ $4 x-12=4(x-3)$ $-2 x+8=2(4-x)$ $x+4=x-1$ $x+2=-3(x+1)$ $2 x+1=2 x+5$ $2(3-x)=2 x-1$

Studdy Solution

STEP 1

1. We are given a list of equations.
2. We need to determine which of these equations have no solutions.

STEP 2

1. Simplify each equation.
2. Analyze the simplified equation to determine if it has no solutions.
3. Identify all equations with no solutions.

STEP 3

Simplify each equation individually.
Equation 1: $5x - 5 = x$
Subtract $x$ from both sides:
$5x - x - 5 = 0$
$4x - 5 = 0$
Equation 2: $3(x+4) = 3x + 10$
Distribute on the left side:
$3x + 12 = 3x + 10$
Equation 3: $4x - 12 = 4(x-3)$
Distribute on the right side:
$4x - 12 = 4x - 12$
Equation 4: $-2x + 8 = 2(4-x)$
Distribute on the right side:
$-2x + 8 = 8 - 2x$
Equation 5: $x + 4 = x - 1$
Subtract $x$ from both sides:
$4 = -1$
Equation 6: $x + 2 = -3(x+1)$
Distribute on the right side:
$x + 2 = -3x - 3$
Equation 7: $2x + 1 = 2x + 5$
Subtract $2x$ from both sides:
$1 = 5$
Equation 8: $2(3-x) = 2x - 1$
Distribute on the left side:
$6 - 2x = 2x - 1$

STEP 4

Analyze each simplified equation to determine if it has no solutions.
Equation 1: $4x - 5 = 0$
Solve for $x$ :
$4x = 5$
$x = \frac{5}{4}$
This equation has a solution.
Equation 2: $3x + 12 = 3x + 10$
Subtract $3x$ from both sides:
$12 = 10$
This is a contradiction, so there are no solutions.
Equation 3: $4x - 12 = 4x - 12$
This is an identity, so there are infinitely many solutions.
Equation 4: $-2x + 8 = 8 - 2x$
This is an identity, so there are infinitely many solutions.
Equation 5: $4 = -1$
This is a contradiction, so there are no solutions.
Equation 6: $x + 2 = -3x - 3$
Solve for $x$ :
$x + 3x = -3 - 2$
$4x = -5$
$x = -\frac{5}{4}$
This equation has a solution.
Equation 7: $1 = 5$
This is a contradiction, so there are no solutions.
Equation 8: $6 - 2x = 2x - 1$
Solve for $x$ :
$6 + 1 = 2x + 2x$
$7 = 4x$
$x = \frac{7}{4}$
This equation has a solution.

STEP 5

Identify all equations with no solutions.
Equations with no solutions are:
- Equation 2: $3(x+4) = 3x + 10$ - Equation 5: $x + 4 = x - 1$ - Equation 7: $2x + 1 = 2x + 5$
The equations with no solutions are:
$\boxed{3(x+4) = 3x + 10, \, x + 4 = x - 1, \, 2x + 1 = 2x + 5}$

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