Algebraic Expressions


An expression is a meaningful collection of numbers, variables, and signs, positive or negative, of operations that must make mathematical and logical sense. Expressions:
  • contain any number of algebraic terms
  • use signs of operation—addition, subtraction, multiplication, and division.
  • do not contain an equality sign (=)
An example of an expression is:

–3ax + 11wx2y===Equations===
An equation is a statement that two numbers or expressions are equal.

Watch the following video, copy the questions of the test in your notebook

Solution of an Equation

When an equation has a variable, the solution to the equation is the number that makes the equation true when we replace the variable with its value.
We say y = 3 is a solution to the equation 4 × y + 7 = 19, for replacing each occurrence of y with 3 gives us
4 × 3 + 7 = 19 ==>
12 + 7 = 19 ==>
19 = 19 which is true.

Simplifying Equationsniñamatemat.png

To find a solution for an equation, we can use the basic rules of simplifying equations. These are as follows:
  1. You may evaluate any parentheses, exponents, multiplications, divisions, additions, and subtractions in the usual order of operations. .
  2. You may combine like terms. This means adding or subtracting variables of the same kind. The expression 2x + 4x simplifies to 6x. The expression 13 - 7 + 3 simplifies to 9.
  3. You may add any value to both sides of the equation.
  4. You may subtract any value from both sides of the equation. This is best done by adding a negative value to each side of the equation.
  5. You may multiply both sides of the equation by any number except 0.
  6. You may divide both sides of the equation by any number except 0.
Hint: Since subtracting any number is the same as adding its negative, it can be helpful to replace subtractions with additions of a negative number.
Do the following test
Test 1
Test 2
Test 3 (Choose level 4 and solve x)
5.- Now you can play this game
Game about algebraic reasoning

Word problems as equations


When converting word problems to equations, certain "key" words tell you what kind of operations to use: addition, multiplication, subtraction, and division. The table below shows some common phrases and the operation to use.
As an equation
The sum of my age and 10 equals 27.
y + 10 = 27
The difference between my age and my younger sister's age, who is 11 years old, is 5 years.
y - 11 = 5
The product of my age and 14 is 168.
y × 14 = 168
Three times my age is 60.
3 × y = 60
less than
Seven less than my age equals 32.
y - 7 = 32
The total of my pocket change and 20 dollars is $22.43.
y + 20 = 22.43
more than
Eleven more than my age equals 43.
11 + y = 43