Solving Equations

Solving Equations

Steps to Solving Equations​

2(x+4) + 2 ​= 4x + 5 + 2x

​

1. ​Distribute if needed: 2(x+4) ---> 2x+8

2. Combine like terms: add up all the variables, add up all the constants.​

   2x + 8 + 2​ = 4x +2x + 5 ------> 2x +10 = 6x +5

3. Use inverse operations to add or subtract so that you end up with one constant term.

   ​

4. Use inverse operations to add or subtract so that you end up with one variable.

   ​

5. ​Divide the constant by the coefficient that is attached to the variable.

​ ​

1. Go to "calculate" under the scratchpad

2. Press the menu key

3. Press the number 3: Algebra, then the number 1​: Numerical Solve

4. Inside the parenthesis type in the equation EXACTLY as you see it. Make sure to add a comma with whatever variable you are solving for.

​

nSolve​ ( 2(x+4) + 2 ​= 4x + 5 + 2x , x )

​

5. ​Press "enter" and the calculate will solve for the variable that you asked for.

Solving Equations Using nSolve

Multiple Choice

Solve for x.

3x+4 =2x-7

• x = 11

• x = -11

• x = 11/5

• x = 5/11

Multiple Choice

Solve for x.

6x - 10x - 11 = 8x - 2x + 2

• x = 4

• x = -1.3

• x = 1/4

• x = -6

Multiple Choice

Solve the equation that is displayed in the model.

• -4

• -2

• 4

• 2

​Writing Equations/Inequalities from Word Problems

• ​Look for key words that represent the variable term: per, each, every, an, rate

• Look for key words or phrases that represent the constant term: Initial fee, starting, down payment, up front, down payment

• Look for key words that represent symbols: equal to, same as, less than, more than, greater than, no more than, no less than, fewer than, larger than, etc.

• Look for key words that mean add or subtract: decr​ease by, increase by, spends, saves, plus, minus, additional, descending, ascending.

Multiple Choice

Lucy rents a bike from a company that charges an initial fee of $12 plus $3 per hour that the bike is rented. If Lucy spends $30, write an equation that can be used to represent how many hours she can rent the bike.

• 3x - 12 = 30

• 3x + 12 =30

• 3x = 30 + 12

• 30 - 3x = 12

Multiple Choice

Write an inequality that matches the following word problem:

Tess has 42 words of an essay typed and is typing about 1.3 words per second. Margo has 122 words of an essay typed and is erasing about 1.2 words per second. In how many seconds will the number of words in Tess’s essay exceed the number of words in Margo’s essay?

• 42 - 1.3x > 122 - 1.2x

• 42 + 1.3x > 122 - 1.2x

• 42 +1.2x < 122 - 1.3x

• 42 - 1.3x < 122 - 1.2x