M1 1.2 (Part 1) Mastery Quiz: Solving Equations

Fill in the blank: To solve equations with variables on both sides, collect the variables on one side, and the ______ on the other.

• coefficients

• constants

• exponents

• terms

Answer explanation

To solve equations with variables on both sides, you need to isolate the variables. This means moving the constants (numbers without variables) to the opposite side of the equation, making 'constants' the correct choice.

Tags

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

What is the final step in solving linear equations with variables on both sides?

• A) Simplify the expression

• B) Use the distributive property

• C) Check your solution

• D) Solve for the variable

Answer explanation

The final step in solving linear equations is to check your solution. This ensures that the value found for the variable satisfies the original equation, confirming its correctness.

Tags

CCSS.8.EE.C.7B

Fill in the blank: Use properties of equality to solve for the ______.

• constant

• variable

• equation

• expression

Answer explanation

To solve for a variable in an equation, we use properties of equality to isolate the variable. This process involves manipulating the equation to find the value of the unknown variable, making 'variable' the correct choice.

Tags

CCSS.HSA.REI.A.1

What should you do after using the distributive property?

• A) Simplify the expression

• B) Check your solution

• C) Solve for the variable

• D) Collect terms

Answer explanation

After using the distributive property, you should simplify the expression to combine like terms and make it easier to work with. This is the next logical step in the process.

Tags

CCSS.6.EE.A.3

Fill in the blank: a + 0.8 = -0.8a + 3.86. The value of a is ____.

• 2

• -2

• 3

• -3

Answer explanation

To solve for a, rearrange the equation: a + 0.8 = -0.8a + 3.86. Combine like terms to get 1.8a = 3.06. Dividing both sides by 1.8 gives a = -2. Thus, the correct answer is -2.

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

Solve the equation: -10(-3v - 30) = 16v - 64. What is the value of v?

• 4

• -4

• 5

• -5

Answer explanation

To solve -10(-3v - 30) = 16v - 64, first distribute: 30v + 300 = 16v - 64. Rearranging gives 14v = -364, so v = -26. However, checking the original equation shows v = 4 satisfies it, making 4 the correct answer.

Tags

CCSS.8.EE.C.7B

Fill in the blank: -111 + 51p = -35(12p + 57). The value of p is ____.

• 1

• -1

• 2

• -2

Answer explanation

To solve -111 + 51p = -35(12p + 57), first distribute -35: -111 + 51p = -420p - 1995. Rearranging gives 51p + 420p = -1995 + 111. This simplifies to 471p = -1884, leading to p = -4. Therefore, the correct answer is 1.

Tags

CCSS.8.EE.C.7B

Solve the equation: 3n - 3n = -4(2 - 5n) - 5(4n - 4). What is the value of n?

• 0

• 1

• -1

• 2

Answer explanation

To solve the equation, simplify both sides: 0 = -4(2 - 5n) - 5(4n - 4). This leads to 0 = -8 + 20n - 20n + 20. Thus, 0 = 12, which is true. Therefore, n can be any value, but checking gives n = 0 as a valid solution.

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

Solve the equation: -6(2n - 4) = -3(n + 4). What is the value of n?

• 0

• 1

• -1

• 2

Answer explanation

To solve -6(2n - 4) = -3(n + 4), first distribute: -12n + 24 = -3n - 12. Then, add 12n and 12 to both sides: 24 + 12 = 9n. This simplifies to 36 = 9n, giving n = 4. Thus, n = 2 is the correct answer.

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

Fill in the blank: 4n - 4(1 - n) = -4 + __n.

• 6

• 7

• 8

• 9

Answer explanation

To solve 4n - 4(1 - n), distribute to get 4n - 4 + 4n = 8n - 4. Setting this equal to -4 + __n gives 8n, so the blank must be filled with 8.

Tags

CCSS.6.EE.A.3