Problem 15
Question
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.
Step-by-Step Solution
Verified Answer
The number 'x' is 14.
1Step 1: 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 \(2(4 + x) = 36\).
2Step 2: 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 \(8 + 2x = 36\)
3Step 3: 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, \(x = 14\).
Other exercises in this chapter
Problem 14
Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2} b h\) for \(h\)
View solution Problem 14
Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$3(3 z+5)-7=89$$
View solution Problem 15
Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$-2=x+14$$
View solution Problem 15
Express the solution set of each inequality in interval notation and graph the interval. \(x>\frac{5}{2}\)
View solution