Problem 20
Question
Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Five more than four times a number is that number increased by \(35 .\) Find the number.
Step-by-Step Solution
Verified Answer
The solution to the equation is \(x = 10\).
1Step 1: Translate the English Statement into an Algebraic Equation
The statement 'Five more than four times a number is that number increased by 35' can be translated into the equation \(4x + 5 = x + 35 \). Here, 'four times a number' is represented as \(4x\), 'five more than' as '+5', 'that number increased by 35' is written as \(x + 35\)
2Step 2: Solve the Equation
Rearrange the equation by bringing like terms together. This can be done by subtracting \(x\) from both sides to get \(3x + 5 = 35\) and then subtracting \(5\) from both sides to isolate \(3x\) on one side of the equation, which gives \(3x = 30\).
3Step 3: Solve for x
Finally, to solve for \(x\), divide both sides of the equation by \(3\) to get \(x = 10\).
Other exercises in this chapter
Problem 20
Solve each equation in Exercises \(15-26\) by the square root method. $$(x-3)^{2}=36$$
View solution Problem 20
In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(3, \infty)$$
View solution Problem 20
Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x}{5}-\frac{1}{2}=\frac{x}{6} $$
View solution Problem 21
In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{2}{3-i}$$
View solution