Algebra Assignments

Topic: Solving Linear Equations and Inequalities

Part 1: Solving Linear Equations

1. Solve for x:

   a) 2x+5=152x + 5 = 152x+5=15

   b) 3(x?2)=4x+13(x - 2) = 4x + 13(x?2)=4x+1

   c) 5x?7=2x+85x - 7 = 2x + 85x?7=2x+8

   d) 2x3?4=10frac{2x}{3} - 4 = 1032x?4=10

2. Word Problem:

   Sarah has twice as many apples as John. If Sarah gives John 4 apples, she will have 6 more apples than John. How many apples do Sarah and John each have initially? Formulate the problem as a linear equation and solve for the number of apples each has.

Part 2: Solving Linear Inequalities

1. Solve the following inequalities:

   a) 3x?7<2x>

   b) 4(x?3)?2x+64(x - 3) geq 2x + 64(x?3)?2x+6

   c) 5?2x?x+15 - 2x leq x + 15?2x?x+1

   d) x+12>3x?4frac{x + 1}{2} > 3x - 42x+1>3x?4

2. Graph the solution on a number line for each inequality in Part 2.

Part 3: Systems of Linear Equations

1. Solve the following systems of equations using the substitution or elimination method:

   a) {2x+3y=7x?y=4begin{cases} 2x + 3y = 7 x - y = 4 end{cases}{2x+3y=7x?y=4

   b) {3x?y=52x+4y=10begin{cases} 3x - y = 5 2x + 4y = 10 end{cases}{3x?y=52x+4y=10

   c) {x+y=62x?3y=?1begin{cases} x + y = 6 2x - 3y = -1 end{cases}{x+y=62x?3y=?1

2. Word Problem:

   Two friends, Alice and Bob, are saving money. Alice saves $5 every day, while Bob saves $7 every day. If Bob already has $50 saved up and Alice has $20, after how many days will they have saved the same amount of money? Set up a system of linear equations and solve it.

Part 4: Application of Linear Equations

1. Problem:

   A car rental company charges a flat fee of $50 plus $0.25 per mile driven. If a customer has $100 to spend, what is the maximum number of miles they can drive? Formulate the problem as a linear equation and solve.

Part 5: Challenge Question

1. Problem:

   If the sum of three consecutive even numbers is 54, what are the numbers? Use algebraic methods to find the solution.

Instructions:

• Show all your work and provide explanations for each step.
• Graphs should be neatly drawn and labeled.
• Make sure to double-check your answers before submitting.

If you need any further details or another type of algebra assignment, feel free to ask!

Are you struggling to keep up with the demands of your academic journey? Don't worry, we've got your back!
Exam Question Bank is your trusted partner in achieving academic excellence for all kind of technical and non-technical subjects. Our comprehensive range of academic services is designed to cater to students at every level. Whether you're a high school student, a college undergraduate, or pursuing advanced studies, we have the expertise and resources to support you.

To connect with expert and ask your query click here Exam Question Bank