Question

linear equations w/ distribution (day 2)
item 1/3 possibly iwo
question
solve for x:
-2(-x + 1) + 2x - 4 = 34

Explanation:

Step1: Distribute -2

We use the distributive property \(a(b + c)=ab+ac\) to expand \(-2(-x + 1)\). So, \(-2\times(-x)+(-2)\times1 = 2x-2\). The equation becomes \(2x - 2+2x - 4=34\).

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(2x+2x = 4x\). For the constant terms: \(-2-4=-6\). The equation is now \(4x-6 = 34\).

Step3: Add 6 to both sides

To isolate the term with \(x\), we add 6 to both sides of the equation. \(4x-6 + 6=34 + 6\), which simplifies to \(4x=40\).

Step4: Divide by 4

Divide both sides of the equation by 4 to solve for \(x\). \(\frac{4x}{4}=\frac{40}{4}\), so \(x = 10\).

Answer:

\(x = 10\)