Problem 115 - Introductory Algebra for College Students

Question

Solve: \(5 x+28=6-6 x\). (Section \(2.2,\) Example 7 )

Step-by-Step Solution

Answer

The solution to the equation is \(x = -2\).

Step 1: Combine like terms

The first step is to get all terms with \(x\) to one side of the equation and constants to the other side. To do this, add \(6x\) to both sides of the equation and subtract \(28\) from both sides. This gives: \(5x + 6x = 6 - 28.\)

Step 2: Simplify equation

Simplify both sides of the equation. On the left side, add \(5x\) and \(6x\) to get \(11x\). On the right side, subtract \(28\) from \(6\) to get \(-22\). The equation now becomes: \(11x = -22\).

Step 3: Solve for \(x\)

Lastly, to isolate \(x\) on one side of the equation, divide both sides by \(11\). This gives: \(x = -22 / 11\).