Alright, let's solve each of these equations step-by-step.
### Equation 1:
[tex]\[ -20 = -4x - 6x \][/tex]
First, simplify the right side by combining like terms:
[tex]\[ -20 = -10x \][/tex]
To solve for [tex]\( x \)[/tex], divide both sides by [tex]\(-10\)[/tex]:
[tex]\[ x = \frac{-20}{-10} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solution for [tex]\( x \)[/tex] is:
[tex]\[ x = 2 \][/tex]
### Equation 2:
[tex]\[ 8x - 2 = -9 + 7x \][/tex]
First, get all the [tex]\( x \)[/tex]-terms on one side and the constants on the other side. Subtract [tex]\( 7x \)[/tex] from both sides:
[tex]\[ 8x - 7x - 2 = -9 \][/tex]
[tex]\[ x - 2 = -9 \][/tex]
Next, add 2 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = -9 + 2 \][/tex]
[tex]\[ x = -7 \][/tex]
So, the solution for [tex]\( x \)[/tex] is:
[tex]\[ x = -7 \][/tex]
### Equation 3:
[tex]\[ 4m - 4 = 4m \][/tex]
Subtract [tex]\( 4m \)[/tex] from both sides to see if you have a consistent equation:
[tex]\[ 4m - 4m - 4 = 4m - 4m \][/tex]
[tex]\[ -4 = 0 \][/tex]
Since this statement is clearly false ([tex]\(-4\)[/tex] does not equal [tex]\( 0 \)[/tex]), this equation has no solution.
### Equation 4:
[tex]\[ 5p - 14 = 8p + 4 \][/tex]
First, move all the [tex]\( p \)[/tex]-terms to one side and the constants to the other side by subtracting [tex]\( 8p \)[/tex] from both sides and adding 14:
[tex]\[ 5p - 8p - 14 = 4 \][/tex]
[tex]\[ -3p - 14 = 4 \][/tex]
Next, add 14 to both sides to isolate the term with [tex]\( p \)[/tex]:
[tex]\[ -3p = 4 + 14 \][/tex]
[tex]\[ -3p = 18 \][/tex]
To solve for [tex]\( p \)[/tex], divide both sides by [tex]\(-3\)[/tex]:
[tex]\[ p = \frac{18}{-3} \][/tex]
[tex]\[ p = -6 \][/tex]
So, the solution for [tex]\( p \)[/tex] is:
[tex]\[ p = -6 \][/tex]
### Summary of Solutions:
1. [tex]\( x = 2 \)[/tex]
2. [tex]\( x = -7 \)[/tex]
3. No solution
4. [tex]\( p = -6 \)[/tex]
