Question

solve each equation.

1. 11v - 6(4 + 3v) = -12(2v + 8) - v
2. 2(p - 1) - (9p - 2) = -
3. -3 + 8(6x - 11) = 6(8x - 3) + 1
4. 9 - n + 12n + 11 =

Explanation:

Problem 9: Solve \( 11v - 6(4 + 3v) = -12(2v + 8) - v \)

Step 1: Distribute the terms

First, we need to distribute the -6 on the left side and the -12 on the right side.
Left side: \( 11v - 6\times4 - 6\times3v = 11v - 24 - 18v \)
Right side: \( -12\times2v - 12\times8 - v = -24v - 96 - v \)
So the equation becomes: \( 11v - 24 - 18v = -24v - 96 - v \)

Step 2: Combine like terms

Left side: Combine the \( v \) terms: \( 11v - 18v = -7v \), so left side is \( -7v - 24 \)
Right side: Combine the \( v \) terms: \( -24v - v = -25v \), so right side is \( -25v - 96 \)
Now the equation is: \( -7v - 24 = -25v - 96 \)

Step 3: Add \( 25v \) to both sides

To get all the \( v \) terms on one side, we add \( 25v \) to both sides.
\( -7v + 25v - 24 = -25v + 25v - 96 \)
\( 18v - 24 = -96 \)

Step 4: Add 24 to both sides

To isolate the term with \( v \), we add 24 to both sides.
\( 18v - 24 + 24 = -96 + 24 \)
\( 18v = -72 \)

Step 5: Divide both sides by 18

To solve for \( v \), we divide both sides by 18.
\( \frac{18v}{18} = \frac{-72}{18} \)
\( v = -4 \)

Step 1: Distribute the terms

Left side: Distribute the 8: \( -3 + 8\times6x - 8\times11 = -3 + 48x - 88 \)
Right side: Distribute the 6: \( 6\times8x - 6\times3 + 1 = 48x - 18 + 1 \)
So the equation becomes: \( -3 + 48x - 88 = 48x - 18 + 1 \)

Step 2: Combine like terms

Left side: Combine the constant terms: \( -3 - 88 = -91 \), so left side is \( 48x - 91 \)
Right side: Combine the constant terms: \( -18 + 1 = -17 \), so right side is \( 48x - 17 \)
Now the equation is: \( 48x - 91 = 48x - 17 \)

Step 3: Subtract \( 48x \) from both sides

Subtract \( 48x \) from both sides: \( 48x - 48x - 91 = 48x - 48x - 17 \)
\( -91 = -17 \)

Wait, this is a contradiction. \( -91 \) is not equal to \( -17 \), so there is no solution for this equation.

Answer:

\( v = -4 \)

Problem 11: Solve \( -3 + 8(6x - 11) = 6(8x - 3) + 1 \)