Question

solve each equation. \\(-(-2x + 1) = 9 - 14x\\)

Explanation:

Step1: Simplify the left side

Using the distributive property \( -(-a + b)=a - b \), we have \( -(-2x + 1)=2x-1 \). So the equation becomes \( 2x - 1=9 - 14x \).

Step2: Add \( 14x \) to both sides

Adding \( 14x \) to both sides to get all \( x \) terms on the left: \( 2x+14x - 1=9 - 14x+14x \), which simplifies to \( 16x - 1=9 \).

Step3: Add 1 to both sides

Adding 1 to both sides: \( 16x - 1 + 1=9 + 1 \), so \( 16x=10 \).

Step4: Divide by 16

Divide both sides by 16: \( x=\frac{10}{16}=\frac{5}{8} \).

Answer:

\( x = \frac{5}{8} \)