Question

1. what is the solution to: 10(2x + 6) = -4x - 45 - 18x

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we have \(10(2x + 6)=10\times2x+10\times6 = 20x+60\).

Step2: Combine like terms on the right side

Combine the \(x\) - terms: \(-4x-18x=-22x\), so the right side becomes \(-22x - 45\).

Step3: Set up the new equation

Now our equation is \(20x + 60=-22x-45\).

Step4: Add \(22x\) to both sides

Adding \(22x\) to both sides gives \(20x+22x + 60=-22x+22x-45\), which simplifies to \(42x+60=-45\).

Step5: Subtract 60 from both sides

Subtracting 60 from both sides: \(42x+60 - 60=-45 - 60\), so \(42x=-105\).

Step6: Divide both sides by 42

Divide both sides by 42: \(x=\frac{-105}{42}\), and simplifying the fraction (dividing numerator and denominator by 21) gives \(x =-\frac{5}{2}=-2.5\).

Answer:

\(x =-\frac{5}{2}\) (or \(x=-2.5\))