Ohio State University Graphing Ordered Pairs and Linear Equations Problems

Homework 10 – Graphing Ordered Pairsand Linear Equations
Name: _____________________________
1. Graph each of the ordered pairs on the same set of axes. Label each point with the corresponding
letter.
A: (1, 2)
B: (−2, 3)
C: (4.5, −4)
D: (0, 2)
3
2
E: ( , 0)
2. Graph the equation by finding two points on the line.
3𝑥 + 2𝑦 = 8
x
y
3. Graph the equation.
𝑦 = −2.5
Homework 8 – Solving Equations with Rational Expressions
Name: ___________________
Solve each of the equations for the variable. Place your answer on the line provided.
1.
10
𝑥
5
= 𝑥−2
1. _____________________
2. If 4 U.S. dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 U.S.
dollars?
2. _______________________
3. Crayola can make 2400 crayons in 4 minutes. How many can be made in 15 minutes?
3. _______________________
4.
5.
4.
𝑥
3
−4=
3
𝑥
3
3
2𝑥+3
12
2𝑥
1
− 4 = 12 + 4
12
𝑥−4
3𝑥
= 6 + 𝑥−4
4. _______________________
5. _______________________
4. _______________________
5.
5
2𝑥
− 5 = 𝑥−6
𝑥−6
5. _______________________
Homework 9 – Solving Inequalities
Name: _____________________________
Solve each of the inequalities for the variable. Place your answer on the line provided.
1.
2𝑥 + 5 − 3 ≤ 6
1. _______________________
2.
−3(7 − 𝑥) ≥ 1 + 5𝑥 − 12
2. _______________________
3.
13 − 7𝑥 ≥ 10𝑥 − 4
3. _______________________
4.
−3(2𝑥 + 1) > −2(𝑥 + 4)
4. _______________________
5.
−4 < 3𝑥 + 2 ≤ 18 5. _______________________ STAT0086 Co-Requisite – Lesson 8 Solving Equations with Rational Expressions Some equations involve rational expressions. With solving such equations, we would first want to multiply each term by the least common multiple of each denominator in order to “clear” the fraction component of the problem. You will see then that the equation becomes just like those previously solved. Just be sure to double check for extraneous solutions – those that cause the fraction to be undefined. Recall that undefined is when the denominator is equal to 0. If the equation is a proportion (one rational expression on each side of the equal sign), then you can also use the method of cross-multiplication. Examples: Solve for x in each equation. 1) 2) 3) 2 15 21 𝑥+4 6 8 = 3𝑥 7 =8 5 = 𝑥+7 𝑥−4 4) Jared ran 10 miles in 80 minutes. At that rate how far would he run in 2.5 hours? 5) Mel fills his gas tank with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it cost to fill an 18 gallon tank? 6) 𝑥−2 3 − 𝑥−3 5 13 = 15 7) 8) 2+𝑥 4 − 5𝑥−2 12 = 8−2𝑥 5 2𝑥 9 +3= 𝑥−2 𝑥−2 2𝑥 4 9) 3 + 𝑥−3 = 𝑥−3 10) 6 𝑥−3 2𝑥 + 1 = 𝑥−3