## Blog Introduction:

Welcome students! If you’re working on lesson 7 problem set 5.1, then you’re probably looking for some help with the answers. Whether your teacher has provided you with some guidance or you’re looking to double-check your work, this post has got your back! In this blog, we’ll be going over some of the common problems in the problem set and providing you with the solutions you need. So, sit back, relax, and get ready to ace your next assignment!

### Blog Body:

#### Problem #1 – Evaluating an Expression

The first problem in the problem set asks you to evaluate the given expression: 6a – 4b, where a = -3 and b = 5. To solve the problem, simply substitute the given values for a and b into the expression, and perform the operations. Our answer is 6(-3) – 4(5) = -18 – 20 = -38.

#### Problem #2 – Arithmetic Sequence

The second problem asks you to write down the next three terms in the sequence 2, 5, 8, 11, . . . The sequence is an arithmetic sequence because each term is found by adding 3 to the previous term. Therefore, the next three terms are 14, 17, and 20.

#### Problem #3 – Solving a Linear Equation

The third problem requires you to solve a simple linear equation: 5 + 3x = 17. To solve the equation, first subtract 5 from both sides, giving you 3x = 12. Then, divide both sides by 3, giving you x = 4.

#### Problem #4 – Perimeter of a Rectangle

Problem 4 is a word problem. It asks you to find the perimeter of a rectangle with sides of length 2x + 5 and x + 4. To solve the problem, use the formula for the perimeter of a rectangle, which is P = 2l + 2w. Substituting the given expressions for l and w, we get P = 2(2x + 5) + 2(x + 4) = 6x + 18.

#### Problem #5 – Solving an Equation

The last problem in the problem set asks you to solve the equation 8x – 3 = 5x + 8. To solve the equation, you have to isolate the variable on one side of the equation. First, subtract 5x from both sides, giving you 3x – 3 = 8. Then, add 3 to both sides, giving you 3x = 11. Finally, divide both sides by 3, giving you x = 11/3.

### Conclusion:

Hopefully, this post has helped you work through some of the common problems in lesson 7 problem set 5.1. Remember, practice makes perfect, and the more you engage with math problems, the better you’ll get! Always pay attention to the instructions and the given formulas to ensure you’re following the right steps. Keep going, and good luck in your future mathematical endeavors!