Question

analyze the worked example. then, solve each equation for x.

1. -8x + 7 + 6x = 9

combine like terms to rewrite the equation in two - step form.
□ + 7 = 9
follow steps to isolate the variable
x =

1. 1 = 3x - 0 + 17x

Explanation:

Problem 1: Solve \(-8x + 7 + 6x = 9\)

Step 1: Combine like terms

Combine the \(x\)-terms: \(-8x + 6x = -2x\). So the equation becomes \(-2x + 7 = 9\).

Step 2: Subtract 7 from both sides

Subtract 7 from each side: \(-2x + 7 - 7 = 9 - 7\), which simplifies to \(-2x = 2\).

Step 3: Divide by -2

Divide both sides by \(-2\): \(\frac{-2x}{-2} = \frac{2}{-2}\), so \(x = -1\).

Step 1: Combine like terms

Combine the \(x\)-terms: \(3x + 17x = 20x\). The equation becomes \(1 = 20x - 9\).

Step 2: Add 9 to both sides

Add 9 to each side: \(1 + 9 = 20x - 9 + 9\), which simplifies to \(10 = 20x\).

Step 3: Divide by 20

Divide both sides by 20: \(\frac{10}{20} = \frac{20x}{20}\), so \(x = \frac{1}{2}\) (or \(0.5\)).

Answer:

\(x = -1\)

Problem 2: Solve \(1 = 3x - 9 + 17x\)