Question

solve for x.
2(-2x - 5) - 3x + 2 = 20

Explanation:

Step1: Expand the brackets

Using the distributive property \(a(b + c)=ab+ac\), we expand \(2(-2x - 5)\) to get \(-4x-10\). So the equation becomes \(-4x - 10-3x + 2 = 20\).

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(-4x-3x=-7x\). For the constant terms: \(-10 + 2=-8\). So the equation simplifies to \(-7x-8 = 20\).

Step3: Isolate the \(x\)-term

Add 8 to both sides of the equation to isolate the term with \(x\). \(-7x-8 + 8=20 + 8\), which simplifies to \(-7x=28\).

Step4: Solve for \(x\)

Divide both sides by \(-7\): \(\frac{-7x}{-7}=\frac{28}{-7}\), so \(x = - 4\).

Answer:

\(x=-4\)