Question

directions: show all steps of your thinking and circle final answers!
problem #1 (mild)
solve:
4x + 6 - 7x + 9 = 18
problem #2 (mild)
solve:

• 3(2x - 8) = - 12

problem #3 (mild)
solve:
27 = 46 + 2x - x
problem #4 (mild)
solve:

• 3(2x - 4) = 6x + 12

Explanation:

Problem #1

Step1: Combine like terms

Combine the \(x\)-terms (\(4x - 7x\)) and the constant terms (\(6 + 9\)):
\(4x - 7x + 6 + 9 = 18\)
\(-3x + 15 = 18\)

Step2: Subtract 15 from both sides

Subtract 15 to isolate the \(x\)-term:
\(-3x + 15 - 15 = 18 - 15\)
\(-3x = 3\)

Step3: Divide by -3

Divide both sides by \(-3\) to solve for \(x\):
\(\frac{-3x}{-3} = \frac{3}{-3}\)
\(x = -1\)

Step1: Distribute \(-3\)

Apply the distributive property to \(-3(2x - 8)\):
\(-3(2x) + (-3)(-8) = -12\)
\(-6x + 24 = -12\)

Step2: Subtract 24 from both sides

Subtract 24 to isolate the \(x\)-term:
\(-6x + 24 - 24 = -12 - 24\)
\(-6x = -36\)

Step3: Divide by -6

Divide both sides by \(-6\) to solve for \(x\):
\(\frac{-6x}{-6} = \frac{-36}{-6}\)
\(x = 6\)

Step1: Combine like terms

Simplify \(2x - x\) on the right side:
\(27 = 46 + x\)

Step2: Subtract 46 from both sides

Subtract 46 to solve for \(x\):
\(27 - 46 = 46 + x - 46\)
\(-19 = x\)

Answer:

\(x = -1\)

Problem #2