# Algebra

Good morning - my son has chapter test tomorrow and on linear equations. I would love to be able to help him study, unfortunately is been a while since I've done linear equations and my knowledge is sketchy at best.

Attached is a study guide that he will be using to study from. Can you please solve the equations and provide a brief description of how you solved the equation (note the explanation is very important part of the exercise so that I will be able to explain it to him what needs to be done).

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#### Solution Preview

hi dear, find solutions attached.

Chapter 3: Linear Equations and Functions

Algebra 1 Review

Name __________________ Date __________

Teacher ________________ Per ___________

Solve the equation. Round the result to the nearest hundredth, if necessary.

1. 11 + x = 21 2. 6 - ½x = 10

2

3. x + 3 - 4x = 12 + 2x 4. 3(x - 3) = x -(-2x + 9)

5. -12x + 15 = 0 6. 3.2x + 1.8 = -2.4x - 5.3

7. 8x - 2(3x + 1) = -(7x + 3) 8. Ax + By = C; for x

Rewrite the equations so that y is a function of x. Then create a function table for x = -2, -1, 0, 1.

9. 10x - y = 5 10. 2x + y = 5 - x 11. 3x - (2y + 3) = 1

x y

-2

-1

0

1

x Y

-2

-1

0

1

x y

-2

-1

0

1

Write an equation for each word problem. Solve the equation to answer the question.

12. The selling price of a pair of pants is $45. If the store profits $9.50 for each pair of pants they sell, then what price did the store pay for each pair of pants?

13. You estimate that you spend $475 on groceries each month. How much money do you spend on groceries each week (assume there are 4 weeks in a month)?

18. Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). Find the three consecutive integers whose sum is 47.

19. A local gym charges nonmembers $15 per hour to use the tennis courts. Members pay a yearly fee of $400 plus only $5 per hour for using the tennis courts. Write and solve an equation to determine if you should become a member.

SOLUTIONS:

Hi dear, I think that to be concise and to present the solutions in a way that will be easy to understand, I should use your problems to illustrate what to do in each case. Just bear in mind that in solving any equation, we are looking for something (say x) which we want to put on one side of the '=' sign, and every other thing on the opposite side of it. Say for your question 1 below, we are having 11 and X/2 on one side of the equation and 21 on the opposite side, our interest will be to make sure that we move every other thing except x over to the opposite side, and by so doing we'll have solved that equation. Having that at the back of your mind we can proceed.

SOLUTION 1. 11 + X/2 = 21

Here we are looking for x, so we'll first have to move 11 away from the same side of the equation as x is. We do that so by subtracting 11 from both sides to get

11 - 11 + X/2 = 21 - 11

giving us X/2 = 21 - 11

which simplifies to X/2 = 10

we next need to multiply both sides by 2, this is because we want to do away with the '2' that is underneath x (as denominator). Doing that we have

2 * X/2 = 10 * 2

after cancelling out we get x = 10 * 2

and that simplifies to x = 20 (Answer).

SOLUTION 2. 6 - ½x = 10

Here we first have to move 6 to the opposite side (we'll also do this by subtracting 6 from both sides), that gives

6 - 6 - ½x = 10 - 6

giving ...

#### Solution Summary

This is a solution set of algebra problems, illustrating with numerous examples how to solve linear equations, change of subject of formula, substitution, and other algebra problems.