ED660A_KY.6.EE.3 summ eval

Solve the equation below for x:

2(x+1) = 8

• 5

• 3

• -5

• 11

Answer explanation

2(x+1) = 8

The first step is to distribute the 2 through on the left side to get:

2x + 2 = 8

Then, subtract 2 from both sides:

2x + 2 = 8

- 2 -2

On the left, 2-2=0; on the right, 8-2=6

2x = 6

Divide both sides by 2

x = 3

The first step in solving the equation 5 (x-1) = 0 is to subtract 1 from both sides.

• True
• False

Answer explanation

5 (x-1) = 0

Incorrect. The first step is to distribute the 5 on the left side:

5x - 5 = 0

Next, add 5 to both sides

5x - 5 = 0

• +5 +5

-5+5=0; 0+5 = 5

5x = 5

Lastly, divide both sides by 5, leaving

x = 1

Solve 5 (x-1) = 0

• 0

• -4

• 4

• 1

Answer explanation

The first step is to distribute the 5 on the left side:

5x - 5 = 0

Next, add 5 to both sides

5x - 5 = 0

• +5 +5

-5+5=0; 0+5 = 5

5x = 5

Lastly, divide both sides by 5, leaving

x = 1

The ______ property means that if a = b, then b may be substituted for a in any expression containing a.

If aa=bb, then bb=aa. This is the symmetric property of equality.

• True
• False

Solve the equation for x:

4 (x-1) = x +11

• 5

• 12

• 0

• 15

Answer explanation

4 (x-1) = x +11

First, distribute on the left side

4x - 4 = x + 11

Subtract x on both sides -

3x - 4 = 11

Add 4 to both sides -

3x = 15

Divide both sides by 3 -

x = 5

Solve for x.

3(x - 5) = 0

Evaluate responses using AI:

OFF

Answer explanation

3(x - 5) = 0

Distribute on the left -

3x - 15 = 0

Add 15 to both sides -

3x = 15

Divide both sides by 3 -

x = 5

In solving this equation, what property/properties are used?

a = c and c = 5

2a (x - 1) = 0

2(5) (x-1) = 0

10(x-1) = 0

10x - 10 = 0

10x = 10

x = 1

• symmetric

• substitution

• division

• distributive

Answer explanation

First is substitutive - a = c = 5

2a(x-1) = 0 becomes

2*5 (x-1) = 0

10 (x-1) = 0

Next is distributive on the left - distribute 10

10x - 10 = 0

Solve the equation 2(x-1) + 3(x - 4) = 1

Evaluate responses using AI:

OFF

Answer explanation

2(x-1) + 3(x-4) = 1

Distribute -

2x - 2 + 3x - 12 = 1

Combine like terms (the x's and the numbers) on the left -

5x - 14 = 1

Add 14 to both sides -

5x = 15

Divide both sides by 5 -

x = 3

Solve for y:

3(2-y) = 0

• 2

• 3

• 6

• 0

Answer explanation

3(2-y) = 0

First, distribute 3 on the left side:

6 - 2y = 0

Add 2y to both sides -

6 = 2y

Divide both sides by 2 -

3 = y