Question

example 2 solving a multi-step equation
solve 8x - 6x - 25 = -35. -4n - 8n + 17 = 23

10 = 3n + 20 - n 2k - 6 - 7 + 3k = -48

Explanation:

Step1: Solve \(8x - 6x - 25 = -35\)

Combine like terms: \(8x - 6x = 2x\), so the equation becomes \(2x - 25 = -35\).
Add 25 to both sides: \(2x - 25 + 25 = -35 + 25\), which simplifies to \(2x = -10\).
Divide both sides by 2: \(\frac{2x}{2} = \frac{-10}{2}\), so \(x = -5\).

Step2: Solve \(-4n - 8n + 17 = 23\)

Combine like terms: \(-4n - 8n = -12n\), equation is \(-12n + 17 = 23\).
Subtract 17 from both sides: \(-12n + 17 - 17 = 23 - 17\), so \(-12n = 6\).
Divide by -12: \(\frac{-12n}{-12} = \frac{6}{-12}\), \(n = -\frac{1}{2}\).

Step3: Solve \(10 = 3n + 20 - n\)

Combine like terms: \(3n - n = 2n\), equation is \(10 = 2n + 20\).
Subtract 20: \(10 - 20 = 2n + 20 - 20\), \(-10 = 2n\).
Divide by 2: \(\frac{-10}{2} = \frac{2n}{2}\), \(n = -5\).

Step4: Solve \(2k - 6 - 7 + 3k = -48\)

Combine like terms: \(2k + 3k = 5k\), \(-6 - 7 = -13\), equation is \(5k - 13 = -48\).
Add 13: \(5k - 13 + 13 = -48 + 13\), \(5k = -35\).
Divide by 5: \(\frac{5k}{5} = \frac{-35}{5}\), \(k = -7\).

Answer:

For \(8x - 6x - 25 = -35\), \(x = -5\);
For \(-4n - 8n + 17 = 23\), \(n = -\frac{1}{2}\);
For \(10 = 3n + 20 - n\), \(n = -5\);
For \(2k - 6 - 7 + 3k = -48\), \(k = -7\)