Question

6(4x + 5) = 3x - 4(-4x - 1) + 5

Explanation:

Step1: Expand both sides

First, expand the left - hand side using the distributive property \(a(b + c)=ab+ac\). For \(6(4x + 5)\), we get \(6\times4x+6\times5 = 24x+30\).

Then, expand the right - hand side. First, expand \(-4(-4x - 1)\) using the distributive property \(a(b + c)=ab + ac\) (here \(a=-4\), \(b=-4x\), \(c = - 1\)), we have \(-4\times(-4x)+(-4)\times(-1)=16x + 4\). Then the right - hand side of the equation \(3x-4(-4x - 1)+5\) becomes \(3x + 16x+4 + 5\). Combine like terms: \(3x+16x=19x\) and \(4 + 5=9\), so the right - hand side is \(19x+9\).

Now our equation is \(24x + 30=19x+9\).

Step2: Isolate the variable \(x\)

Subtract \(19x\) from both sides of the equation: \(24x-19x + 30=19x-19x+9\). Simplify both sides: \(5x+30 = 9\).

Then subtract 30 from both sides: \(5x+30 - 30=9 - 30\). Simplify both sides: \(5x=-21\).

Step3: Solve for \(x\)

Divide both sides of the equation by 5: \(x=\frac{-21}{5}=-4.2\)

Answer:

\(x =-\frac{21}{5}\) (or \(x=-4.2\))