Solving Equations With Variables on Both Sides

• Subtracting 4 from both sides.

• Multiplying both sides by 3.

• Adding 4 to both sides

• Dividing both sides by 3.

Answer explanation

If we first divide everything by -2, we are left with;

3x + 4 = 16.

So the last step would be to separate the 3 from the x. Since the 3 is currently multiplying x, we would divide by 3.

Tags

CCSS.HSA.REI.A.1

What is the answer?

3x + 2 = -5x + 10

• x = 1

• x = -1

• x = 6

• x = -6

Answer explanation

If we add 5x to both sides, we get;

8x + 2 = 10.

Then we need to subtract 2 from both sides to get;

8x = 8.

Finally we divide both sides by what is attached to the x, which in this case is 8.

8x/8 = x and 8/8 = 1 so x=1

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

If I wanted to start to simplify this equation what would I do in order to get variables on one side and constants on the other?

2x - 6 = 3x

• Move the 2x to the other side of the equation by adding it to both sides.

• Move the 6 to the other side of the equation by adding it to both side.

• Move the 2x to the other side of the equation by subtracting it from both sides.

• Move the 6 to the other side of the equation by subtracting it from both sides.

Answer explanation

If we move the 2x, then all terms with a variable will be on the right, and all constants will be on the left. Since the 2x is positive on the left, we want to do the opposite and subtract it from both sides.

Tags

CCSS.6.EE.A.3

CCSS.6.EE.B.5

CCSS.6.EE.B.7

What property did I use from step 1 to step 2?

Step 1: 2(x + 3) + 7 = 10x - 11

Step 2: 2x + 6 + 7 = 10x - 11

• Distributive Property

• Combine like terms

• Addition Property of Equality

• Subtraction Property of Equality

Answer explanation

From step 1 to step 2 notice the parantheses go away. Tha tis because

Tags

CCSS.HSA.REI.A.1

• Subtraction Property of Equality

• Distributive Property

• Addition Property of equality

• Combine Like Terms

• Division Property of Equality

Answer explanation

To get rid of the parentheses w use the distributive property.

Then to simplify each side, we combine like terms.

Next the variable terms were all moved to the right side of the equation. The 4x was subtracted from both sides, hence the subtraction property of equality.

Next, we needed to get the constants on the opposite side of the equation, so we added 5 to both sides, hence the addition property of equality.

Finally we used the division prperty and divided both sides by what was attached to the x, which in this case was a 3. We used the division property of equality to get an answer of 1/3 = x.

Tags

CCSS.HSA.REI.A.1

Use the distributive property to simplify the following, fill in the blank with the correct number. Be sure to look closely at what was already written out for you.

-3(2x + 5) = -9x

-6x + _=-9x

Answer explanation

Because there is a -3 otside of the parentheses and a positive 5 inside, when we use the distributive property properly, -3*5 = -15.

Tags

CCSS.6.EE.A.3

Solve for x.

-3(2x + 5) = -9x

• x = 1

• x = 5

• x = -1

• x = -5

Answer explanation

-3(2x + 5) = -9x

-6x - 15 = -9x distribute -3 to the 2x and 5.

-15 = -3x add 6x to both sides

5 = x Divide both sides by -3.

Tags

CCSS.8.EE.C.7B

How do you feel about solving equations with variables on both sides? What is difficult? What do you find easy?

Tags

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7