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Algebra: equations and inequalities

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1. Evaluate: 7 -|(-3)(2) - 2|

2. Simplify: 7x - (4 - 2x)

3. Ross jogs at a rate of one mile every 0.25 hours. At what rate is he jogging in miles per hour?

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

5. Solve for x:
(1/2) x - 1/3 = (1/4) x+ 1/6

6. Solve for x:
2x- 3 = ax

7. Solve: |3x-9|=3

8. Solve the inequality: (2/5) y < 2 or y -2 <11

9. Solve the inequality: 3x > 0 and x -5 < 2

10. Find the slope of the line through each pair of points:
(-1, -4) and (-2, 3)

11. Write the equation of this line in the slope-intercept form:
the line through (-1 , 4) with slope 2/3

12.Graph this inequality
3x + 2y > 5 Graph:

13.Solve the system:
x - 3y= 15
4x+ y= 8

14.Solve the system:
2x-y =22
-x + 3y= -15

15.Graph each system:
y>x+5
y< 3x -

Graph:
X Y

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Solving linear, absolute value equations and inequalities is shown in the solution. The expert writes equations in slope-intercept form.

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1. Evaluate: 7 -|(-3)(2) - 2|
7- I -6-2 I
7 - I-8I
7-8 = -1

2. Simplify: 7x - (4 - 2x) = 7x-4+2x = 9x -4

3. Ross jogs at a rate of one mile every 0.25 hours. At what rate is he jogging in miles per hour?
1/.25 = x/1
4= x
So the rate is 4 miles/ hour

4. Solve for x:
5(2x-3) =x+3
10x - 15 = x+3
-x +15 -x+15
9x = 18
9 9
x = 2

5. Solve for x:
(1/2) x - 1/3 = (1/4) x+ 1/6
-(1/4)x +1/3 -(1/4)x + 1/3
1/4 x = 3/6
1/4 x = ½
x = 2

6. Solve for x:
2x- 3 = ax
-ax+3 -ax +3
(2-a)x = 3
2-a 2-a
x= 3/ ...

Solution provided by:
Chris Busu, PhD (IP)
Education
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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