Answer :
To find which numbers from the set {1, 2, 3, 4, 5} are solutions to the equation [tex]\(4x + 11 = 23\)[/tex], we can follow a step-by-step approach:
1. Understand the Equation: The equation given is [tex]\(4x + 11 = 23\)[/tex]. This means that if you take four times a number [tex]\(x\)[/tex] and add 11 to it, the result should be 23.
2. Isolate the Variable: To solve for [tex]\(x\)[/tex], we first need to isolate it. Start by subtracting 11 from both sides of the equation:
[tex]\[
4x + 11 - 11 = 23 - 11
\][/tex]
This simplifies to:
[tex]\[
4x = 12
\][/tex]
3. Solve for [tex]\(x\)[/tex]: Now, divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{12}{4} = 3
\][/tex]
4. Verify the Solution: We have determined that [tex]\(x = 3\)[/tex]. We need to verify this by substituting it back into the original equation:
[tex]\[
4(3) + 11 = 12 + 11 = 23
\][/tex]
Since the left side equals the right side of the equation, [tex]\(x = 3\)[/tex] is indeed a solution.
5. Check Against the Set of Numbers: From the set {1, 2, 3, 4, 5}, the solution 3 fits perfectly.
6. Understand the Descriptions: We should identify which descriptions accurately represent the equation:
- Description A: "If you add eleven to four times a number, you get 23." This matches because [tex]\(4x + 11\)[/tex] equates to 23.
- Description E: "Eleven more than four times a number is 23." This is another way of expressing [tex]\(4x + 11 = 23\)[/tex]. Both descriptions A and E correctly describe the equation.
Therefore, the solution to the equation is [tex]\(x = 3\)[/tex], and the descriptions that fit the equation are A and E.
1. Understand the Equation: The equation given is [tex]\(4x + 11 = 23\)[/tex]. This means that if you take four times a number [tex]\(x\)[/tex] and add 11 to it, the result should be 23.
2. Isolate the Variable: To solve for [tex]\(x\)[/tex], we first need to isolate it. Start by subtracting 11 from both sides of the equation:
[tex]\[
4x + 11 - 11 = 23 - 11
\][/tex]
This simplifies to:
[tex]\[
4x = 12
\][/tex]
3. Solve for [tex]\(x\)[/tex]: Now, divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{12}{4} = 3
\][/tex]
4. Verify the Solution: We have determined that [tex]\(x = 3\)[/tex]. We need to verify this by substituting it back into the original equation:
[tex]\[
4(3) + 11 = 12 + 11 = 23
\][/tex]
Since the left side equals the right side of the equation, [tex]\(x = 3\)[/tex] is indeed a solution.
5. Check Against the Set of Numbers: From the set {1, 2, 3, 4, 5}, the solution 3 fits perfectly.
6. Understand the Descriptions: We should identify which descriptions accurately represent the equation:
- Description A: "If you add eleven to four times a number, you get 23." This matches because [tex]\(4x + 11\)[/tex] equates to 23.
- Description E: "Eleven more than four times a number is 23." This is another way of expressing [tex]\(4x + 11 = 23\)[/tex]. Both descriptions A and E correctly describe the equation.
Therefore, the solution to the equation is [tex]\(x = 3\)[/tex], and the descriptions that fit the equation are A and E.
