Knowledge of algebraic thinking and the coordinate plane - FTCE

Card 0 of 12

Question

What value of makes this a true statement?

Answer

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on , as follows:

Multiplication precedes subtraction in the order of operations, so reverse the subtraction of 12 by adding 12 to both sides:

Now reverse multiplication by 2 by dividing by 2:

$2y \div2 = 78 \div 2$

.

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Question

and .

If , then evaluate .

Answer

If , then can be determined from the equation

first by substituting 18 for :

$a \cdot 18 = 72$

then by dividing both sides by 18 to isolate the :

$a \cdot 18 \div 18= 72 \div 18$

Now, in the other equation, substitute 4 for :

Divide both sides by 4 to isolate the :

$4b \div 4= 56 \div 4$

,

the correct choice.

Compare your answer with the correct one above

Question

Which of the following equations does not describe a line through the point ?

Answer

If the line of an equation passes through , then, if and , the equation should be true. Therefore, we can identify the correct choice by substituting 2 and 6 for and , respectively, in each equation.

True

True

True

True

False

The correct choice is

.

Compare your answer with the correct one above

Question

What value of makes this a true statement?

Answer

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on , as follows:

Multiplication precedes subtraction in the order of operations, so reverse the subtraction of 12 by adding 12 to both sides:

Now reverse multiplication by 2 by dividing by 2:

$2y \div2 = 78 \div 2$

.

Compare your answer with the correct one above

Question

and .

If , then evaluate .

Answer

If , then can be determined from the equation

first by substituting 18 for :

$a \cdot 18 = 72$

then by dividing both sides by 18 to isolate the :

$a \cdot 18 \div 18= 72 \div 18$

Now, in the other equation, substitute 4 for :

Divide both sides by 4 to isolate the :

$4b \div 4= 56 \div 4$

,

the correct choice.

Compare your answer with the correct one above

Question

Which of the following equations does not describe a line through the point ?

Answer

If the line of an equation passes through , then, if and , the equation should be true. Therefore, we can identify the correct choice by substituting 2 and 6 for and , respectively, in each equation.

True

True

True

True

False

The correct choice is

.

Compare your answer with the correct one above

Question

What value of makes this a true statement?

Answer

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on , as follows:

Multiplication precedes subtraction in the order of operations, so reverse the subtraction of 12 by adding 12 to both sides:

Now reverse multiplication by 2 by dividing by 2:

$2y \div2 = 78 \div 2$

.

Compare your answer with the correct one above

Question

and .

If , then evaluate .

Answer

If , then can be determined from the equation

first by substituting 18 for :

$a \cdot 18 = 72$

then by dividing both sides by 18 to isolate the :

$a \cdot 18 \div 18= 72 \div 18$

Now, in the other equation, substitute 4 for :

Divide both sides by 4 to isolate the :

$4b \div 4= 56 \div 4$

,

the correct choice.

Compare your answer with the correct one above

Question

Which of the following equations does not describe a line through the point ?

Answer

If the line of an equation passes through , then, if and , the equation should be true. Therefore, we can identify the correct choice by substituting 2 and 6 for and , respectively, in each equation.

True

True

True

True

False

The correct choice is

.

Compare your answer with the correct one above

Question

What value of makes this a true statement?

Answer

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on , as follows:

Multiplication precedes subtraction in the order of operations, so reverse the subtraction of 12 by adding 12 to both sides:

Now reverse multiplication by 2 by dividing by 2:

$2y \div2 = 78 \div 2$

.

Compare your answer with the correct one above

Question

and .

If , then evaluate .

Answer

If , then can be determined from the equation

first by substituting 18 for :

$a \cdot 18 = 72$

then by dividing both sides by 18 to isolate the :

$a \cdot 18 \div 18= 72 \div 18$

Now, in the other equation, substitute 4 for :

Divide both sides by 4 to isolate the :

$4b \div 4= 56 \div 4$

,

the correct choice.

Compare your answer with the correct one above

Question

Which of the following equations does not describe a line through the point ?

Answer

If the line of an equation passes through , then, if and , the equation should be true. Therefore, we can identify the correct choice by substituting 2 and 6 for and , respectively, in each equation.

True

True

True

True

False

The correct choice is

.

Compare your answer with the correct one above

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