Question

1. $-1 = -3x + 2x$
2. $-3(4r - 8) = -36$

Explanation:

Problem 6: Solve \(-1 = -3x + 2x\)

Step 1: Combine like terms

On the right side, \(-3x + 2x\) can be combined. Since \(-3x + 2x = (-3 + 2)x\), we calculate \(-3 + 2 = -1\), so the equation becomes \(-1 = -x\).

Step 2: Solve for \(x\)

To solve for \(x\), we multiply both sides of the equation \(-1 = -x\) by \(-1\) (or divide both sides by \(-1\)). When we do that, we get \(x = 1\) (because multiplying both sides of an equation by the same non - zero number preserves the equality, and \((-1)\times(-1)=1\) and \((-1)\times(-x)=x\)).

Step 1: Distribute the \(-3\)

Using the distributive property \(a(b - c)=ab - ac\), where \(a=-3\), \(b = 4r\) and \(c = 8\), we have \(-3\times4r-(-3)\times8=-36\). Calculating the products, \(-3\times4r=-12r\) and \(-(-3)\times8 = 24\), so the equation becomes \(-12r+24=-36\).

Step 2: Subtract 24 from both sides

Subtract 24 from both sides of the equation \(-12r + 24=-36\) to isolate the term with \(r\). We get \(-12r+24 - 24=-36 - 24\). Simplifying both sides, \(24-24 = 0\) and \(-36-24=-60\), so the equation is now \(-12r=-60\).

Step 3: Solve for \(r\)

Divide both sides of the equation \(-12r=-60\) by \(-12\). \(\frac{-12r}{-12}=\frac{-60}{-12}\). Since \(\frac{-12r}{-12}=r\) and \(\frac{-60}{-12} = 5\), we find that \(r = 5\).

Answer:

\(x = 1\)

Problem 8: Solve \(-3(4r - 8)=-36\)