Question

1. the model below represents an equation. what value of x makes the equation true? x = -2 1/2 x = -5/6 x = -0.16 x = -0.5 clear all

Explanation:

Step1: Translate the model to an equation

On the left - hand side, we have 4 \(x\)s and 6 \(- 1\)s, so it is \(4x-6\). On the right - hand side, we have 6 \(x\)s and 4 \(1\)s, so it is \(6x + 4\). The equation is \(4x-6=6x + 4\).

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

Subtract \(4x\) from both sides: \(4x-4x-6=6x-4x + 4\), which simplifies to \(-6 = 2x+4\).

Step3: Move the constant terms to one side

Subtract 4 from both sides: \(-6-4=2x+4 - 4\), resulting in \(-10 = 2x\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{-10}{2}=-5/1=- 2.5=-2\frac{1}{2}\).

Answer:

\(x=-2\frac{1}{2}\)