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• Review of Past Work

• #### 3. Finance

• 4. Rational numbers
• 5. Exponentials
• 6. Estimating surds
• 7. Irrational numbers and rounding off

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By: Siyavula

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# Summary and exercises

## Equations and inequalities: Summary and exercises

• A linear equation is an equation where the power of the variable(letter, e.g. xx) is 1(one). A linear equation has at most one solution
• A quadratic equation is an equation where the power of the variable is at most 2. A quadratic equation has at most two solutions
• Exponential equations generally have the unknown variable as the power. The general form of an exponential equation is: ka(x+p)=mka(x+p)=m
• A linear inequality is similar to a linear equation and has the power of the variable equal to 1. When you divide or multiply both sides of an inequality by any number with a minus sign, the direction of the inequality changes. You can solve linear inequalities using the same methods used for linear equations
• When two unknown variables need to be solved for, two equations are required and these equations are known as simultaneous equations. There are two ways to solve linear simultaneous equations: graphical solutions and algebraic solutions. To solve graphically you draw the graph of each equation and the solution will be the co-ordinates of the point of intersection. To solve algebraically you solve equation one, for variable one and then substitute that solution into equation two and solve for variable two.
• Literal equations are equations where you have several letters (variables) and you rearrange the equation to find the solution in terms of one letter (variable)
• Mathematical modelling is where we take a problem and we write a set of equations that represent the problem mathematically. The solution of the equations then gives the solution to the problem.

## End of Chapter Exercises

1. What are the roots of the quadratic equation x2-3x+2=0x2-3x+2=0

?

2. What are the solutions to the equation x2+x=6x2+x=6

?

3. In the equation y=2x2-5x-18y=2x2-5x-18, which is a value of xx when y=0y=0

?

4. Manuel has 5 more CDs than Pedro has. Bob has twice as many CDs as Manuel has. Altogether the boys have 63 CDs. Find how many CDs each person has.

5. Seven-eighths of a certain number is 5 more than one-third of the number. Find the number.

6. A man runs to a telephone and back in 15 minutes. His speed on the way to the telephone is 5 m/s and his speed on the way back is 4 m/s. Find the distance to the telephone.

7. Solve the inequality and then answer the questions: x3-14>14-x4x3-14>14-x4
1. If xâˆˆRxâˆˆR, write the solution in interval notation.
2. if xâˆˆZxâˆˆZ and x<51x<51, write the solution as a set of integers.

8. Solve for aa: 1-a2-2-a3>11-a2-2-a3>1

9. Solve for xx: x-1=42xx-1=42x

10. Solve for xx and yy: 7x+3y=137x+3y=13 and 2x-3y=-42x-3y=-4


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