Question

multiple choice
listen
what is the solution to the equation
-5x - 3 = 2(6 - x)?
a x = -5/3
b x = -5
c x = -2
attempt 1 of 2 submit

Explanation:

Step1: Expand the right - hand side

We use the distributive property \(a(b - c)=ab - ac\). For \(2(6 - x)\), we have \(2\times6-2\times x = 12-2x\). So the equation \(-5x - 3=2(6 - x)\) becomes \(-5x - 3=12-2x\).

Step2: Move the \(x\) terms to one side

Add \(5x\) to both sides of the equation to get all the \(x\) terms on one side. \(-5x - 3+5x=12-2x + 5x\), which simplifies to \(-3=12 + 3x\).

Step3: Isolate the constant term

Subtract 12 from both sides: \(-3-12=12 + 3x-12\), so \(-15 = 3x\).

Step4: Solve for \(x\)

Divide both sides by 3: \(\frac{-15}{3}=\frac{3x}{3}\), which gives \(x=-5\).

Answer:

B. \(x = - 5\)