© a very good teacher 2007 exit level taks preparation unit objective 4

© A Very Good Teacher 2007

Exit Level

TAKS Preparation UnitObjective 4


Writing Equations and Inequalities

4, Ac3A

• Identify if the situation warrants an equation (=) or an inequality (<, >, ≤, ≥).

• Equations are used when quantities are equal.

• Inequalities are used when quantities are not equal.Look for words like: No more than

No less than

At least

At most


Writing Equations and Inequalities, cont…

• Example: A used car salesman is paid a salary of $200 per week plus at least a 10% commission. If x represents the salesman’s total sales, which of the following could be used to determine y, the salesman’s weekly income?

• Equation or Inequality?The words “at least” indicate that this will be an inequality.

4, Ac3A

Now write the inequality. y ? 200 + .10x

Total income Salary + Commission

Could be greater than or exactly

≥


Solving Equations and Inequalities

• Write the equation or inequality (if necessary)• Substitute any given values• Remember to use inverse operations to

solve• Example: Hanna makes necklaces that she sells at

a local craft show. She pays $50 a day to rent the booth and each necklace costs $3.50 to make. If she sells each necklace for $9, how many necklaces does she need to sell to make a profit during a 3 day weekend at the craft show?

1. Write the equation Profit = 9x – (3.5x + 50(3))

4, Ac3B


Solving Equations and Inequalities, cont…• Now that we have an equation, we can

substitute any given values

• We can replace ‘profit’ with zero to find the break even point

Profit = 9x – (3.5x + 50(3))

0 = 9x – (3.5x + 50(3)) Now Solve 0 = 9x – 3.5x - 50(3)

0 = 9x – 3.5x - 150 0 = 5.5x - 150

+150 +150

150 = 5.5x 5.5 5.5

27.27 = x

4, Ac3B


Solving Equations and Inequalities, cont…

• The most important part of solving equations involving word problems is checking for reasonableness

• According to our equation x = 27.27

• Can Hanna sell 27.27 necklaces?• So the answer must be a whole number

• Is it 27?• No, selling 27 necklaces would not make a profit

• The answer is 28 necklaces!

4, Ac3B


Writing Systems of Equations

• Most systems are comprised of 2 types of equations

• A total equation that represents the total number of items

• And a comparison equation that represents the relationship between the two variables

• Identify what the variables represent

• Identify which numbers go with each equation type.

4, Ac4A


Writing Systems of Equations, cont…• Example: Claudia purchased 12 shirts and jeans

for the school year. Jeans cost $22 and shirts cost $15. If Claudia spent a total of $215, write a system of equations that could be used to find the number of shirts that Claudia purchased.

4, Ac4A

Total Equation Comparison Equation

j + s = 12 22j + 15s = 215


Solving Systems of Equations

• The solution to a system of linear equations is the point where the two lines intersect.

• If you are unsure how to solve a problem by substitution, elimination, or graphing, you can substitute each answer choice into the equations to see which one works for BOTH equations.

4, Ac4B


Solving Systems of Equations, cont…

• Example: The equations of two lines are 4x – y = 3 and y = 5x – 2. What is the value of x in the solution for this system of equations?

4, Ac4B

A. x = -2

B. x = -1

C.x = 2

D.x = 1

4x – y = 3 y = 5x - 2

4(-2) – y = 3-8 – y = 3

+8 +8

– y = 11

y = -11

y = 5(-2) - 2

y = -10 - 2

y = -12

Now try the other answers to see which one works for BOTH equations!

© a very good teacher 2007 exit level taks preparation unit objective 4

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