Expressions and Equations Review

If 3(x + 4) = 3x + 12, what can be said about the equation?

• It has one solution

• It has no solution

• It has infinite solutions.

Answer explanation

The equation 3(x + 4) = 3x + 12 simplifies to the same expression on both sides, indicating that it holds true for all values of x. Therefore, it has infinite solutions.

Tags

CCSS.8.EE.C.7A

Simplify the expression: 6x - 2(3x - 4). What is the simplified form?

• 6x - 6x + 8

• 6x - 6x - 8

• 6x + 6x - 8

• 6x + 6x + 8

Answer explanation

To simplify 6x - 2(3x - 4), first distribute -2: 6x - 6x + 8. The 6x and -6x cancel out, leaving 8. Thus, the simplified form is 6x - 6x + 8, which matches the correct answer.

Tags

CCSS.6.EE.A.3

What is the simplified form of the expression: 7y - 2(3y + 1)?

• y - 2

• y + 2

• -y - 2

• -y + 2

Answer explanation

First, distribute -2: 7y - 6y - 2. Combine like terms: (7y - 6y) - 2 = y - 2. The correct answer is -y - 2.

Tags

CCSS.6.EE.A.3

Solve the equation 5x + 3 = 2x + 15. What is the value of x?

• x = 3

• x = 4

• x = 5

• x = 6

Answer explanation

To solve 5x + 3 = 2x + 15, first subtract 2x from both sides: 3x + 3 = 15. Then, subtract 3: 3x = 12. Finally, divide by 3: x = 4. Thus, the correct answer is x = 4.

If 5x + 3 = 2x + 15, what is the first step to solve for x?

• Add 3 to both sides

• Subtract 2x from both sides

• Subtract 3 from both sides

• Add 2x to both sides

Answer explanation

To isolate x, the first step is to eliminate the 2x on the right side. Subtracting 2x from both sides simplifies the equation to 3x + 3 = 15, making it easier to solve for x.

What is the result of distributing in the equation 4(x + 2)?

• 4x + 2

• 4x + 8

• 8x + 4

• 8x + 2

Answer explanation

To distribute in the equation 4(x + 2), multiply 4 by both x and 2. This gives 4x + 8. Therefore, the correct answer is 4x + 8.

Tags

CCSS.6.EE.A.3

Which equation is equivalent to 5x + 3 = 2x + 15 after subtracting 2x from both sides?

• 3x + 3 = 15

• 5x = 2x + 12

• 3x = 12

• 5x + 3 = 15

Answer explanation

Subtracting 2x from both sides of 5x + 3 = 2x + 15 gives 3x + 3 = 15. Simplifying this further leads to 3x = 12, which matches choice C. Thus, the correct answer is C) 3x = 12.

What is the result of simplifying 4(2x - 3) + 7?

• 8x - 5

• 8x + 5

• 8x - 12

• 8x + 12

Answer explanation

To simplify 4(2x - 3) + 7, first distribute: 4*2x - 4*3 + 7 = 8x - 12 + 7. Then combine like terms: -12 + 7 = -5. The final result is 8x - 5, which matches the correct answer.

Tags

CCSS.6.EE.A.3

What is the solution to the equation 3(x - 2) = 2(x + 1)?

• x = 8

• x = 7

• x = 6

• x = 5

Answer explanation

To solve 3(x - 2) = 2(x + 1), first distribute: 3x - 6 = 2x + 2. Then, isolate x: 3x - 2x = 2 + 6, leading to x = 8. Thus, the correct answer is x = 8.

What is the explanation for no solution in the equation 7x - 3 = 7x + 4?

• Both sides are equal

• Different constants

• Same coefficients

• No variables.

Answer explanation

The equation 7x - 3 = 7x + 4 has the same coefficients for x, but different constants (-3 and +4). This leads to a contradiction, indicating no solution exists. Thus, the correct choice is B) Different constants.

Tags

CCSS.8.EE.C.7A