One-quarter of the difference of a number and 3 is 2. Find the number.(1 point)
Responses
54
5 fourths
20
20
312
3 and 1 half
11
11
proof
To prove that the number is 11, we can use algebraic equations.
Let's assume the number is x.
According to the given information, "One-quarter of the difference of a number and 3 is 2," we can write the equation as:
(1/4)(x - 3) = 2
To solve for x, we can first distribute the 1/4 to the terms inside the parentheses:
(x/4) - (3/4) = 2
Next, we can add (3/4) to both sides of the equation to isolate x:
(x/4) = 2 + (3/4)
Combining the terms on the right side:
(x/4) = 8/4 + 3/4
(x/4) = 11/4
Now, to solve for x, we can multiply both sides by 4:
4(x/4) = 4(11/4)
x = 44/4
Simplifying:
x = 11
Therefore, the number is 11.
Solve 23(x −6)=14 (1 point)
Responses
−27
negative 27
−15
negative 15
15
15
27
27
To solve the equation 23(x - 6) = 14, we can use algebraic steps.
First, distribute the 23 to the terms inside the parentheses:
23x - 138 = 14
Next, isolate the term with the variable by adding 138 to both sides of the equation:
23x = 14 + 138
Combine the terms on the right side:
23x = 152
Finally, solve for x by dividing both sides of the equation by 23:
x = 152/23
Simplifying the fraction, we get:
x ≈ 6.61
Therefore, the solution to the equation is approximately 6.61.
Solve 2/3(x −6)=14 (1 point)
Responses
−27
negative 27
−15
negative 15
15
15
27
27
To solve the equation (2/3)(x - 6) = 14, we can use algebraic steps.
First, distribute the 2/3 to the terms inside the parentheses:
(2/3)x - 12/3 = 14
Simplify the equation:
(2/3)x - 4 = 14
Next, isolate the term with the variable by adding 4 to both sides of the equation:
(2/3)x = 14 + 4
Combine the terms on the right side:
(2/3)x = 18
Finally, solve for x by multiplying both sides of the equation by 3/2:
(3/2)(2/3)x = (3/2)(18)
Simplifying:
x = 27/2
Therefore, the solution to the equation is 27/2, which can also be written as 13.5.
olve 23(x −6)=14 (1 point)
Responses
−27
negative 27
−15
negative 15
15
15
27
To solve the equation 23(x - 6) = 14, we can use algebraic steps.
First, distribute the 23 to the terms inside the parentheses:
23x - 138 = 14
Next, isolate the term with the variable by adding 138 to both sides of the equation:
23x = 14 + 138
Combine the terms on the right side:
23x = 152
Finally, solve for x by dividing both sides of the equation by 23:
x = 152/23
Simplifying the fraction, we get:
x ≈ 6.61
Therefore, the solution to the equation is approximately 6.61.
−27
negative 27
−15
negative 15
15
15
27