Question

Maria solved an equation as shown below.

3 (x + 6) = 5 (x minus 4). 3 x + 18 = 5 x minus 20. 38 = 2 x. 19 = x.

What is the solution to Maria’s equation?
19
38
no solution
infinitely many solutions
Answer
The expression on the left side of an equation is shown below.

Negative 6 x + 6 = box

If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
–6
1
Negative 6 x
Negative 6 x + 6
Answer
incorrect
Answer
Jeremy wants to determine the number of solutions for the equation below without actually solving the equation.

Negative 3 (x + 1) + 3 x = negative 3 (x minus 1) + 3

Which method should Jeremy use?
Determine whether the equation has the form a = a, and if it does, the equation has infinitely many solutions.
Determine whether the equation has the form a = b, and if it does, the equation has no solution.
Determine whether the equation has the form x = a, and if it does, the equation has one solution.
Determine whether the equation has the form x = 0, and if it does, the equation has no solution.
Answer
LaShawn solved the equation below to the determine the solution.

3 x minus 8 = negative x + 4 (x minus 2)

How many solutions does LaShawn’s equation have?
zero
one
two
infinitely many
Answer
Chelsea wrote several equations and determined that only one of the equations has exactly one solution. Which of these equations has exactly one solution?
4 (x + 3) = 7 x minus 6
4 (x + 3) + 8 = 4 x + 20
4 (x + 3) + 3 x + 7 x + 12
4 (x + 3) + 6 = 4 x + 9
Answer
The equation below has one solution.

9 x minus 10 = 3 x + 2

What is the solution to the equation?
–2
–1
1
2
Answer
Isaac wants the equation below to have no solution when the missing number is placed in the box.

Box (x + 2) + 2 x = 2 (x + 6) + 4 x

Which number should he place in the box?
2
4
6
8
Answer
The expression on the left side of an equation is shown below.

Negative 5 (x + 2) + 3 x = box

If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
Negative 5 (x minus 3) + 2 x
–5x – 10
xMinus 2 x + 2 + 3 x
Negative 2 (x + 5)
Answer
The expression on the left side of an equation is shown below.

Negative 4 (x minus 2) + 5 x = box

If the equation has no solution, which expression can be written in the box on the other side of the equation?
2(x + 4) – x
x + 8
4(x + 2) – 5x
x
Answer
Dante wrote several equations and determined that only one of the equations has infinitely many solutions. Which of these equations has infinitely many solutions?
6 (x + 3) + x = 7 x + 2 + 1
6 (x + 3) + x = 7 x + 5
6 (x + 3) + x = 6 x + 3 + 15
6 (x + 3) + x = 7 x + 9 + 9
Answer
Kari picked 23 bunches of flowers from her garden. Each bunch had the same number of flowers. After she gave 46 flowers away, she had 138 left. How many flowers were in each bunch?
Answer
Aanya wrote the four equations that are shown below.

A

6 x minus 8 = 4 (x minus 2) + 2 x
B

3 (x minus 1) + 2 x = 3 (x minus 1) + 2

C

7 x + 2 minus x = 6 (x + 2)
D

4 (x + 3) + x = 5 (x + 1) + 7

She examined them, without solving them, to determine which has exactly one solution. Which of Aanya’s equations has exactly one solution?
Answer
choose a awnser for the previous question 6 x minus 8 = 4 (x minus 2) + 2 x
3 (x minus 1) + 2 x = 3 (x minus 1) + 2
7 x + 2 minus x = 6 (x + 2)
4 (x + 3) + x = 5 (x + 1) + 7
Answered by Bot
19
Answered by Bot
Negative 6 x
Answered by Bot
I'm sorry about that! The correct answer is "Negative 6 x + 1".

Here's an explanation:

If the equation has an infinite number of solutions, this means that whatever we put in the box on the right side of the equation will make the equation true for all values of x.

Let's try putting -6x in the box. -6x + 6 = -6x + 6 is a true statement, so this would work. However, this would only work for x = 0. For any other value of x, the equation -6x + 6 = -6x + 6 would not be true.

Let's try putting 1 in the box. -6x + 6 = 1 is equivalent to -6x = -5, which simplifies to x = 5/6. So this would work, but it's only one solution.

The expression -6x + 6 is one possibility that would work, because we can simplify the equation to -6x + 6 = -6x + 6, which is true for all values of x.

Therefore, the correct answer is Negative 6 x + 1.
Answered by Bot
Determine whether the equation has the form a = a, and if it does, the equation has infinitely many solutions.
Answered by Bot
one
Answered by Bot
4 (x + 3) + 6 = 4 x + 9.
Answered by Bot
1
Answered by Bot
-6 should be placed in the box.

Here's the explanation:

Box (x + 2) + 2x = 2(x + 6) + 4x

First, let's simplify both sides of the equation:

Box(x + 2) + 2x = 2(x + 6) + 4x

Box x + 2Box + 2x = 2x + 12 + 4x

Box x + 2Box + 2x = 6x + 12

Next, let's combine like terms:

Box x + 2Box + 2x - 6x = 12

Box x + 2Box - 4x = 12

Box(x - 2) - 4x = 12

Box(x - 2 - 4) = 12

Box(x - 6) = 12

Now, we want to find what number in the box will make this equation have no solution. In other words, there is no value of x that will make the equation true.

If we simplify the equation further, we get:

x - 6 = 0

x = 6

However, if we put 6 in the box, we get:

6(x + 2) + 2x = 2(x + 6) + 4x

48 = 0

This is not true, so x = 6 does not work.

Let's try putting -6 in the box:

-6(x + 2) + 2x = 2(x + 6) + 4x

-24 = -24

This is a true statement, and it is the only solution that will make this equation have no solution, because if we use any other number than -6 in the box, we will get one solution for x when we solve the equation.
Answered by Bot
Negative 2 (x + 5).
Answered by Bot
4(x + 2) - 5x.
Answered by Bot
6(x + 3) + x = 6x + 3 + 15.
Answered by Bot
Let's start the problem by using "x" to represent the number of flowers in each bunch.

Kari picked 23 bunches of flowers, so she originally had:

23x

After she gave 46 flowers away, she had:

23x - 46

And we're told that she had 138 flowers remaining:

23x - 46 = 138

Let's solve for x:

23x - 46 = 138

23x = 184

x = 8

Therefore, there were 8 flowers in each bunch.
Answered by Bot
Equation B has exactly one solution.
Answered by Bot
Equation B - 3 (x minus 1) + 2 x = 3 (x minus 1) + 2 - has exactly one solution.