Algebraic Equations

Question 1

What is the goal of algebraic equations?

Answer 1

To find out the value of the variable by ‘reverse engineering’ the equation.

Question 2

How do you solve equations?

Answer 2

Invert all the operations to cancel out each operation, so that you are only left with the variable on the one side and the answer on the other side.

Question 4

What must you do when solving an algebraic equation?

Answer 4

Simplify both sides
Move exponents to the one side
Use SAMDEB
Remember all your exponent and integer rules

Question 6

What is the golden rule of algebraic equations?

Answer 6

What you do to the one side you do to the other.

Question 7

What happens when you have variables on both sides of the equal sign?

Answer 7

You must move all the variables by changing their sign i.e. If it is a negative it will become a positive, if it is a positive it will become a negative.

Question 9

What is the order of operations when solving algebraic equations?

Answer 9

Since solving equations is working out sums backwards, the order is the opposite of BEDMAS
Subtraction
Addition
Multiplication
Division
Exponents
Brackets

Question 10

What happens when we square root a number?

Answer 10

The result must be written with a plus minus sign, since the variable can be either negative or positive for the equation to work.

Question 11

How do we solve equations where the variable is the exponent?

Answer 11

We need to make the bases the same. For instance, 5 to the power of c is equal to 25. 5 to the power of c and 5squared have the same bases, so c must be equal to 2.

Question 12

How do you solve equations where there is a fraction?

Answer 12

We need to get rid of the fraction before we can solve the equation. We do this by multiplying the entire equation by the denominator. Remember the golden rule: what we do to the one side we must do to the other, so we must multiply the other side by the denominator as well.

Question 13

How do you solve equations where the unknown is being square rooted?

Answer 13

Since square roots are cancelled out by squares, you must square it. Remember the golden rule: what you do to the one side you must do to the other, so you must square the other side too.

Question 14

How do you solve word equations?

Answer 14

First, figure out what order the terms go in
See what operations are being performed, and where
Write a numerical equation gathered from the steps above
Solve the equation
Give the answer in a sentence