Question

solving linear equations with multiple variables.
x+5 = 3x - 1 3x + 6 = 2x + 7
13x + 50 = 10x + 10 5x - 40 = 3x + 10
3.6w = 1.6w + 24 \\(\frac{7}{10}n + \frac{3}{2} = \frac{3}{2}n + 2\\)
\\(\frac{2}{11}m + 16 = 4 + \frac{6}{11}m\\)

Explanation:

Step1: Solve \( x + 5 = 3x - 1 \)

Subtract \( x \) from both sides: \( 5 = 2x - 1 \)
Add 1 to both sides: \( 6 = 2x \)
Divide by 2: \( x = 3 \)

Step2: Solve \( 3x + 6 = 2x + 7 \)

Subtract \( 2x \) from both sides: \( x + 6 = 7 \)
Subtract 6: \( x = 1 \)

Step3: Solve \( 13x + 50 = 10x + 10 \)

Subtract \( 10x \): \( 3x + 50 = 10 \)
Subtract 50: \( 3x = -40 \)
Divide by 3: \( x = -\frac{40}{3} \)

Step4: Solve \( 5x - 40 = 3x + 10 \)

Subtract \( 3x \): \( 2x - 40 = 10 \)
Add 40: \( 2x = 50 \)
Divide by 2: \( x = 25 \)

Step5: Solve \( 3.6w = 1.6w + 24 \)

Subtract \( 1.6w \): \( 2w = 24 \)
Divide by 2: \( w = 12 \)

Step6: Solve \( \frac{7}{10}N + \frac{3}{2} = \frac{3}{2}N + 2 \)

Multiply by 10 to eliminate denominators: \( 7N + 15 = 15N + 20 \)
Subtract \( 7N \): \( 15 = 8N + 20 \)
Subtract 20: \( -5 = 8N \)
Divide by 8: \( N = -\frac{5}{8} \)

Step7: Solve \( \frac{2}{11}M + 16 = 4 + \frac{6}{11}M \)

Subtract \( \frac{2}{11}M \): \( 16 = 4 + \frac{4}{11}M \)
Subtract 4: \( 12 = \frac{4}{11}M \)
Multiply by \( \frac{11}{4} \): \( M = 33 \)

Answer:

\( x = 3 \) (for \( x + 5 = 3x - 1 \)), \( x = 1 \) (for \( 3x + 6 = 2x + 7 \)), \( x = -\frac{40}{3} \) (for \( 13x + 50 = 10x + 10 \)), \( x = 25 \) (for \( 5x - 40 = 3x + 10 \)), \( w = 12 \) (for \( 3.6w = 1.6w + 24 \)), \( N = -\frac{5}{8} \) (for \( \frac{7}{10}N + \frac{3}{2} = \frac{3}{2}N + 2 \)), \( M = 33 \) (for \( \frac{2}{11}M + 16 = 4 + \frac{6}{11}M \))