3x-(9x-3)=3(4-2x)= 7x-(x+3)=3*(2x-1) 3-5(x-1)=x-2 0,2(x-2)-0,4(x+3)=0,4-0,6x
Let's solve each of the equations step by step.
Equation 1: \( 3x - (9x - 3) = 3(4 - 2x) \)
Expand both sides: \[ 3x - 9x + 3 = 12 - 6x \]
Simplify: \[ -6x + 3 = 12 - 6x \]
Add \( 6x \) to both sides: \[ 3 = 12 \]
This is a contradiction, which means there is no solution.
Equation 2: \( 7x - (x + 3) = 3(2x - 1) \)
Expand both sides: \[ 7x - x - 3 = 6x - 3 \]
Simplify: \[ 6x - 3 = 6x - 3 \]
This means that the left and right sides are identical for all values of \( x \). Thus, this equation has infinitely many solutions.
Equation 3: \( 3 - 5(x - 1) = x - 2 \)
Expand the left side: \[ 3 - 5x + 5 = x - 2 \]
Simplify: \[ 8 - 5x = x - 2 \]
Add \( 5x \) to both sides: \[ 8 = 6x - 2 \]
Add \( 2 \) to both sides: \[ 10 = 6x \]
Divide by \( 6 \): \[ x = \frac{10}{6} = \frac{5}{3} \]
Equation 4: \( 0.2(x - 2) - 0.4(x + 3) = 0.4 - 0.6x \)
Expand the left side: \[ 0.2x - 0.4 - 0.4x - 1.2 = 0.4 - 0.6x \]
Combine like terms: \[ -0.2x - 1.6 = 0.4 - 0.6x \]
Add \( 0.6x \) to both sides: \[ 0.4x - 1.6 = 0.4 \]
Add \( 1.6 \) to both sides: \[ 0.4x = 2 \]
Divide by \( 0.4 \): \[ x = \frac{2}{0.4} = 5 \]
Summary of Solutions:
- No solution.
- Infinitely many solutions.
- \( x = \frac{5}{3} \)
- \( x = 5 \)
