A Quiz About Math

1. Solve! 2x = 3 x = ?

The equation 2x = 3 can be solved by dividing both sides of the equation by 2. This gives us x = 3/2, which is equivalent to 1.5. Therefore, the answer is 1.5.

Explanation

The equation 2x = 3 can be solved by dividing both sides of the equation by 2. This gives us x = 3/2, which is equivalent to 1.5. Therefore, the answer is 1.5.

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2. In the inequality 2x - 1 > 7, x can never be equal to 2!

True

False

In the given inequality 2x - 1 > 7, the goal is to solve for x. To isolate x, we first add 1 to both sides of the inequality, which gives 2x > 8. Then, we divide both sides by 2 to get x > 4. This means that x can take any value greater than 4. Since x cannot be equal to 2, the statement "x can never be equal to 2" is true.

Explanation

In the given inequality 2x - 1 > 7, the goal is to solve for x. To isolate x, we first add 1 to both sides of the inequality, which gives 2x > 8. Then, we divide both sides by 2 to get x > 4. This means that x can take any value greater than 4. Since x cannot be equal to 2, the statement "x can never be equal to 2" is true.

3. Problem Solving The sum of a number and 7 is 33. What is the number?

40

26

25

27

To find the number, we can set up an equation based on the information given. Let's call the number "x". The sum of the number and 7 is equal to 33, so we can write the equation as x + 7 = 33. To solve for x, we can subtract 7 from both sides of the equation. This gives us x = 33 - 7, which simplifies to x = 26. Therefore, the number is 26.

Explanation

To find the number, we can set up an equation based on the information given. Let's call the number "x". The sum of the number and 7 is equal to 33, so we can write the equation as x + 7 = 33. To solve for x, we can subtract 7 from both sides of the equation. This gives us x = 33 - 7, which simplifies to x = 26. Therefore, the number is 26.

4. Jolibee is X years old now... . How old will he bee two years from now?

X - 2

2x

X + 2

X/ 2

Jolibee is currently X years old. Two years from now, he will be X + 2 years old.

Explanation

Jolibee is currently X years old. Two years from now, he will be X + 2 years old.

5. Solve! x - 1 = 3 x = ?

To solve the equation x - 1 = 3, we need to isolate the variable x. To do this, we can add 1 to both sides of the equation. This will cancel out the -1 on the left side, leaving us with x = 4. Therefore, the value of x is 4.

Explanation

To solve the equation x - 1 = 3, we need to isolate the variable x. To do this, we can add 1 to both sides of the equation. This will cancel out the -1 on the left side, leaving us with x = 4. Therefore, the value of x is 4.

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6.

Simplify!

2

2x

1

X

This is an example of addition of similar algebraic fractions. To add this type fractions, simply copy the denominator and add the numerators. See examples from the book and video.

Explanation

This is an example of addition of similar algebraic fractions. To add this type fractions, simply copy the denominator and add the numerators. See examples from the book and video.

7. Illustrate commutative property of addition using the expression (3 + x) + y

Review
Two basic properties of addition:

Commutative property – terms may be switched but it won’t affect its value.

Illustration:
apple + banana = banana + apple
A + B = B + A
Associative property – Changing terms in a grouping is a change in association.

Illustration:
(Lyca + John) + Trish = (Lyca + Trish) + John
(L + J) + T = (L + T) + J

Explanation

Review
Two basic properties of addition:

Commutative property – terms may be switched but it won’t affect its value.

Illustration:
apple + banana = banana + apple
A + B = B + A
Associative property – Changing terms in a grouping is a change in association.

Illustration:
(Lyca + John) + Trish = (Lyca + Trish) + John
(L + J) + T = (L + T) + J

Submit

8.

16

15

9

17

not-available-via-ai

Explanation

not-available-via-ai

9.

Given the figure above. Solve for x, if the to total area is 50 ft².

1 ft

8 ft

7 ft

20 ft

Use the formula: Area = Length x Width
Given:
Area = 50
Length = 5
Width = X + 2

injecting all values into the formula...
A = L * W
50 = 5 (X + 2)

then solve...

50 = 5x + 10

50 - 10 = 5x + 10 - 10

40 = 5x

40/5 = 5x/5

8 = x
or
x = 8

Explanation

Use the formula: Area = Length x Width
Given:
Area = 50
Length = 5
Width = X + 2

injecting all values into the formula...
A = L * W
50 = 5 (X + 2)

then solve...

50 = 5x + 10

50 - 10 = 5x + 10 - 10

40 = 5x

40/5 = 5x/5

8 = x
or
x = 8

10. Below is the solution for solving X + 2 = - ( - 3) and its corresponding property. X + 2 = - ( - 3) Property applied X + 2 = 3 Opposites of opposites property -(- a) = +a X + 2 + ? = 3 + ? Property of Opposites X + 0 = 1 ? X = 1 What's missing above?

-2 and zero property of equality

+2 and zero property of equality

-2 and Identity property of Addition

+2 and Identity property of Addition

Please see explanation in the book... lesson 3-2

Explanation

Please see explanation in the book... lesson 3-2

11. Problem solving Jane paid P pesos, per day, for the replacement of the tiles in her bathroom. If labor cost was 250 pesos a day and each tile costs 15 pesos, how much will it cost her in a day T tiles are used?

P = 15T + 250

T = 15P+ 250

15T=250P

P =

Pattern
Y = ax + b

b = labor cost which is constant per day
a = number of tile which may change depending on how many are used...
Y is the P or the total cost per day..cause it depends on the number of tiles used in a day.
X is the T which independent variable...

Explanation

Pattern
Y = ax + b

b = labor cost which is constant per day
a = number of tile which may change depending on how many are used...
Y is the P or the total cost per day..cause it depends on the number of tiles used in a day.
X is the T which independent variable...

12. On a scale was an apple. Two apples were added per hour. As a result, The weight increased. What model of addition is being illustrated above?

Commutative model of addition

Slide Model

Two dimensional Slide model

Putting together model

*Models of addition

Two models
Putting-together model – putting two or more things together is the same as adding.

Put 2 apples and 3 apples in one.
2 Apples + 3 Apples = 5 Apples
Slide-model- increase in distance or scale on a plane is also addition
My body temperature rose 4 degrees up.
Body temp + 4 degrees

Explanation

*Models of addition

Two models
Putting-together model – putting two or more things together is the same as adding.

Put 2 apples and 3 apples in one.
2 Apples + 3 Apples = 5 Apples
Slide-model- increase in distance or scale on a plane is also addition
My body temperature rose 4 degrees up.
Body temp + 4 degrees

13. Simplify the following expression. 3(x + 2) – 2(x - 3)

X-1

X +12

X

13x

Steps:
Step 1: distribute to remove parenthesis
Step 2: switch all similar terms right next to each other.
Step 3: add similar terms.
Note: we can’t add 3x and 4. 3x has a variable while does not.

Tracing Misconception!
if you answered A:
you need to distribute 3 and -2 to all its corresponding terms inside each pair of parentheses "()"

if you answered c:
you probably forgot to include the sign of 2 in distributing.

if you answered d:
you probably added x + 12. Remember that they are dissimilar terms.

for more info: check video on 3 - 9

Explanation

Steps:
Step 1: distribute to remove parenthesis
Step 2: switch all similar terms right next to each other.
Step 3: add similar terms.
Note: we can’t add 3x and 4. 3x has a variable while does not.

Tracing Misconception!
if you answered A:
you need to distribute 3 and -2 to all its corresponding terms inside each pair of parentheses "()"

if you answered c:
you probably forgot to include the sign of 2 in distributing.

if you answered d:
you probably added x + 12. Remember that they are dissimilar terms.

for more info: check video on 3 - 9

14. The vertices of a triangle are A(1, 1), B(2, -1), and C(-1, 0). Moving all the points 3 units to the left and 1 units up. Locate the image of point B.

4th Quadrant

Y-axis

3rd Quadrant

X-axis

Moving all the points 3 units to the left and 1 unit up would result in the new coordinates for point B being (-1, 0). This means that the image of point B would be located on the X-axis.

Explanation

Moving all the points 3 units to the left and 1 unit up would result in the new coordinates for point B being (-1, 0). This means that the image of point B would be located on the X-axis.

15.

Describe the pattern using an expression.

Y=4x+1

4x+1

Y

X+4

remember

ax + b ....expression
y = ax + b ... equation

a is the increase of the number of circles... and b is the constant circle or the first instance minus the 'a'.

Explanation

remember

ax + b ....expression
y = ax + b ... equation

a is the increase of the number of circles... and b is the constant circle or the first instance minus the 'a'.