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Chapter 2: Problem 15

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Twice the sum of four and a number is \(36 .\) Find the number.

Short Answer

Expert verified
The number 'x' is 14.

Step by step solution

01

Translate the Verbal Expression Into a Mathematical Equation

The expression states twice the sum of four and a number is \(36\). Writing it out mathematically, you get \(2(4 + x) = 36\).
02

Distribute and Simplify the Equation

Use the distributive property to simplify the left side of the equation. This means you multiply the 2 by everything inside the brackets: \(2*4 + 2*x = 36\), which simplifies to \(8 + 2x = 36\)
03

Solve for 'x'

To solve for 'x', first subtract 8 from both sides of the equation. This gives \(2x = 36 - 8\), which simplifies to \(2x = 28\). Then, divide both sides of the equation by 2, resulting in \(x = 28 / 2\). So, \(x = 14\).

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