Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?
The last property of equality that you would use to justify the solution to this problem is the Addition Property of Equality.
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?
Manipulate the equation y=7x−12 so that it is written in terms of x. Which equation is equivalent to y=7x−12?(
To manipulate the equation y = 7x - 12 and write it in terms of x, we isolate the term with x on one side of the equation.
Adding 12 to both sides of the equation, we get:
y + 12 = 7x
Rearranging the equation, we have:
7x = y + 12
Hence, the equation that is equivalent to y = 7x - 12 is: 7x = y + 12.
To solve this problem, we will follow the steps given:
1. Write the equation: "Five less than three-fourths of x is seven" translates to \( \frac{3}{4}x - 5 = 7 \).
2. Substitute x with 16: \( \frac{3}{4}(16) - 5 = 7 \).
3. Simplify: \( 12 - 5 = 7 \).
4. Solve: \( 7 = 7 \).
The last property of equality we would use to justify the solution is the Reflexive Property of Equality, which states that for any real number a, a = a. In this case, we have 7 = 7, so the solution is justified by the Reflexive Property of Equality.
To solve this problem, we first need to write an equation based on the given information.
The problem states that "Five less than three-fourths of x is seven." Let's break it down step by step:
Step 1: Define the unknown value:
Let's use the variable x to represent the unknown value.
Step 2: Express three-fourths of x:
Three-fourths of x can be written as (3/4)x.
Step 3: Subtract five from three-fourths of x:
Five less than three-fourths of x can be expressed as (3/4)x - 5.
Step 4: Set up the equation:
According to the problem, "(3/4)x - 5 is equal to seven." We can write this as:
(3/4)x - 5 = 7.
Now that we have the equation, we can solve for x.
Step 5: Solve the equation:
To isolate x, we need to get rid of the constant term (-5) on the left side of the equation. We can do this by adding 5 to both sides of the equation:
(3/4)x - 5 + 5 = 7 + 5.
Simplifying the equation:
(3/4)x = 12.
To eliminate the coefficient (3/4) in front of x, we can multiply both sides of the equation by its reciprocal, which is 4/3:
(4/3)(3/4)x = (4/3)(12).
Simplifying further:
(x) = 16.
So, we have found that x = 16.
To justify this solution, we can use the Last Property of Equality, which states that if two values are equal and we perform the same operation on both sides of the equation, the equation remains true. In this case, we performed the same operation of adding 5 to both sides, followed by multiplying both sides by 4/3. Hence, the Last Property of Equality justifies the solution to this problem.
The linear equation that can be used to find Andrea's and Tony's current ages is:
a - 6 = (a + 2) / 3