Question

\\-3 = \frac{x}{4} - 1\\
\\\frac{s}{2} - 9 = -19\\
\\\frac{w}{5} - 3 = 0\\
\\-4n + 9 = -35\\
\\-3 + 7n = 137\\
\\-3 - 9y = 69\\

Explanation:

Identify the equations

We have six independent linear equations to solve.

• Equation 1: \(-3 = \frac{x}{4} - 1\)
• Equation 2: \(\frac{s}{2} - 9 = -19\)
• Equation 3: \(\frac{w}{5} - 3 = 0\)
• Equation 4: \(-4n + 9 = -35\)
• Equation 5: \(-3 + 7n = 137\)
• Equation 6: \(-3 - 9y = 69\)

Solve Equations 1 and 2

Using Two-Step Equations and Algebraic Isolation:
For Equation 1:
Add \(1\) to both sides:

$$-2 = \frac{x}{4}$$

Multiply both sides by \(4\):

$$x = -8$$

For Equation 2:
Add \(9\) to both sides:

$$\frac{s}{2} = -10$$

Multiply both sides by \(2\):

$$s = -20$$

Solve Equations 3 and 4

Using Two-Step Equations and Algebraic Isolation:
For Equation 3:
Add \(3\) to both sides:

$$\frac{w}{5} = 3$$

Multiply both sides by \(5\):

$$w = 15$$

For Equation 4:
Subtract \(9\) from both sides:

$$-4n = -44$$

Divide both sides by \(-4\):

$$n = 11$$

Solve Equations 5 and 6

Using Two-Step Equations and Algebraic Isolation:
For Equation 5:
Add \(3\) to both sides:

$$7n = 140$$

Divide both sides by \(7\):

$$n = 20$$

For Equation 6:
Add \(3\) to both sides:

$$-9y = 72$$

Divide both sides by \(-9\):

$$y = -8$$

Answer:

No.	Problem	Answer
2	\(\frac{s}{2} - 9 = -19\)	\(s = -20\)
3	\(\frac{w}{5} - 3 = 0\)	\(w = 15\)
4	\(-4n + 9 = -35\)	\(n = 11\)
5	\(-3 + 7n = 137\)	\(n = 20\)
6	\(-3 - 9y = 69\)	\(y = -8\)