Question

solving linear equations with multiple variables.
$x + 5 = 3x - 1$ $3x + 6 = 2x + 7$
$13x + 50 = 10x + 110$ $5x - 40 = 3x + 10$
$3.6w = 1.6w + 24$ $\frac{7}{10}n + \frac{3}{2} = \frac{3}{2}n + 2$
$\frac{2}{11}m + 16 = 4 + \frac{6}{11}m$

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 \( 13x + 50 = 10x + 110 \)

Subtract \( 10x \): \( 3x + 50 = 110 \). Subtract 50: \( 3x = 60 \). Divide by 3: \( x = 20 \).

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: \( 7N + 15 = 15N + 20 \). 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:

\( x = 3 \), \( x = 1 \), \( x = 20 \), \( x = 25 \), \( w = 12 \), \( N = -\frac{5}{8} \), \( M = 33 \) (for respective equations)