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Algebra - expressions, equations, inequalities

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State all answers in standard equation format, interval notation, or solution set notation unless otherwise instructed by the problem statement. Also, show the step-by-step process you used to solve the problems.

Simplify the following expression: 0.7(x + 1) - (x - 2)

Mary loves to skip rope. She makes one skip every 0.04 minute. What is her skipping rate in skips per minute?

Solve for x: 3(x - 4) - 1 = 2x + 5

Solve for y:
y
--- - 2 = y + 1
5

Find the dimensions of a rectangle whose length is 50 inches more than its width and whose perimeter is 500 inches.

Solve the inequality: 1 - 2x > 5. Express your answer as solution set.

Solve the inequality: -3 < 2 - 5x < 12. Express the answer as a solution set or a number line.

Write an inequality that describes the graph:

<------(============]----------->
-4 -3 -2 -1 0 1 2

Find the slope of the line which contains the points
(4, 2) and (-1, 7).

Write the slope-intercept form of the equation of the line through (0, -2) that is parallel to the line
5x + 4y = 3.

Graph the line y = 2x - 3

Graph the line 2x + 3y = 6. Develop the equation of a line perpendicular to this line that goes through (0, 0).

Solve the system defined by the equations:
3x - 2y = 11
5x + 3y = 12

Solve the system 2x - 3y = -8 and x + y = 1.

There are 980 students who attend Reklaw High School. At a recent basketball game at the school, 35% of the male students and 40% of the female students were in attendance. The total number of students attending the ball game from Reklaw High was 369. How many males and how many females attend this high school?

Solve the system 3x + 2y = 3 and 4x -3y = -13. Solution method is your choice.

Solve for a: 2a - (3 - 2a) = 5 - 2(1 - a)

0
6
3
-3

Solve the inequality: 2 < 2 - 3x < 5.

0 > x > -5/3
0 < x < -1
x > -1
-1 < x < 0

Find the equation of the line perpendicular to
2y = -x + 3 and which passes through (0, 4).

y = x + 4
y = -1/2x + 4
y = -1/2x + 3/2
y = 2x + 4

Evaluate the following expression using
a = -1,
b = 2 and
c = -3

c 6 b
--- + --- - ---
a b a

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State all answers in standard equation format, interval notation, or solution set notation unless otherwise instructed by the problem statement. Also, show the step-by-step process you used to solve the problems.

1. Simplify the following expression: 0.7(x + 1) - (x - 2)

= 0.7x + 0.7 - x + 2
= 0.7x - x + 0.7 + 2
= -0.3x + 2.7

2. Mary loves to skip rope. She makes one skip every 0.04 minute. What is her skipping rate in skips per minute?
1 skip : 0.04 minute
? skip : 1 minute

1 / 0.04
25 skips per minute.

3. Solve for x: 3(x - 4) - 1 = 2x + 5

3x - 12 - 1 = 2x + 5
3x - 2x = 5 + 12 + 1
X = 18

4. Solve for y:
y
--- - 2 = y + 1
5

y - 10 = 5y + 5
y - 5y = 5 + 10
-4y = 15
y = 15/4
y = 3.75

5. Find the dimensions of a rectangle whose length is 50 inches more than its width and whose perimeter is 500 inches.

L = 50 in + W
P = 500 in

P = 2L + 2W
500 = 2 (50 + W) + 2W
500 = 100 + 2W + 2W
500 = 100 + 4W
500 - 100 = 4W
400 = ...

Solution Summary

This provides examples of working with expressions, equations, and inequalities, including finding lines, word problems, evaluating expressions, and solving.

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