Question

11 -29 - 7x = -1 + 7(-2x + 1)

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \( - 29-7x=-1 + 7(-2x + 1)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 7\), \(b=-2x\) and \(c = 1\), so \(7(-2x + 1)=7\times(-2x)+7\times1=-14x + 7\). The equation becomes \(-29-7x=-1-14x + 7\).

Step2: Simplify the right side

Simplify the right - hand side of the equation \(-29-7x=-1-14x + 7\). Combine the constant terms \(-1\) and \(7\): \(-1 + 7=6\). So the equation is \(-29-7x=6-14x\).

Step3: Add \(14x\) to both sides

To get all the \(x\) terms on one side, we add \(14x\) to both sides of the equation \(-29-7x=6-14x\). \((-29-7x)+14x=(6-14x)+14x\). Simplify both sides: \(-29 + 7x=6\).

Step4: Add 29 to both sides

Add 29 to both sides of the equation \(-29 + 7x=6\). \((-29 + 7x)+29=6 + 29\). Simplify both sides: \(7x=35\).

Step5: Divide both sides by 7

Divide both sides of the equation \(7x = 35\) by 7. \(\frac{7x}{7}=\frac{35}{7}\). So \(x = 5\).

Answer:

\(x = 5\)