Sure, let's solve the given problem step-by-step.
1. Understand the Problem:
- We are given a word statement: "Four more than four times a number is twelve."
- We need to convert this word statement into a mathematical equation.
2. Translate the Word Statement to an Equation:
- Let [tex]\( x \)[/tex] be the unknown number we are trying to find.
- "Four times a number" is mathematically represented as [tex]\( 4x \)[/tex].
- "Four more than four times a number" means we add 4 to [tex]\( 4x \)[/tex], which gives [tex]\( 4x + 4 \)[/tex].
- "Is twelve" means it equals 12.
Therefore, the equation based on the word statement is:
[tex]\[
4x + 4 = 12
\][/tex]
3. Solve the Equation:
- To find the value of [tex]\( x \)[/tex], we isolate it on one side of the equation:
[tex]\[
4x + 4 = 12
\][/tex]
- Subtract 4 from both sides of the equation:
[tex]\[
4x + 4 - 4 = 12 - 4
\][/tex]
Simplifies to:
[tex]\[
4x = 8
\][/tex]
- Divide both sides by 4:
[tex]\[
\frac{4x}{4} = \frac{8}{4}
\][/tex]
Simplifies to:
[tex]\[
x = 2
\][/tex]
4. Verification with Given Set:
- We need to check which solutions from the set [tex]\(\{1, 2, 4, 6, 10\}\)[/tex] satisfy the equation [tex]\( 4x + 4 = 12 \)[/tex].
The solution we found is [tex]\( x = 2 \)[/tex].
- Checking within the set: [tex]\( 2 \)[/tex] is an element of the set [tex]\(\{1, 2, 4, 6, 10\}\)[/tex].
Therefore, the valid solution that satisfies the equation [tex]\( 4x + 4 = 12 \)[/tex] from the given set is [tex]\( x = 2 \)[/tex].
5. Final Answer:
- The equation derived from the word statement is:
[tex]\[
4x + 4 = 12
\][/tex]
- The solution to the equation is:
[tex]\[
x = 2
\][/tex]
- The solution from the given set that satisfies the equation is:
[tex]\[
\{2\}
\][/tex]
