Problem 59 - Introductory Algebra for College Students

Question

$$\text { Solve: } 2(x+3)=24-2(x+4)$$

Step-by-Step Solution

Answer

The solution to the equation is \(x = 2.5\).

Step 1: Distribute the 2

By employing the distributive property, multiply the 2 into each term in the parentheses on each side of the equation to obtain \(2x + 6 = 24 - 2x - 8\).

Step 2: Simplify each side

Simplify each side of the equation in order to gather like terms. On the left, there are no simplifications to be done. On the right, 24-8 results into 16. This yields \(2x + 6 = 16 - 2x\).

Step 3: Group all x terms on one side

To solve for x, all the terms containing x should be grouped on one side of the equation. To do so, add \(2x\) to both sides, resulting into \(4x + 6 = 16\).

Step 4: Isolate x

In order to get x by itself, subtract 6 from both sides of the equation. The equation simplifies to \(4x = 10\).

Step 5: Solve for x

Finally, to solve for x, divide both sides by 4 to isolate x. This gives \(x = 2.5\).