Answer:
Question 1:
The letter x or any letter used when writing an expression is representative of unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea
Question 2:
The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7
Question 3:
In the first expression, the like terms are;
10y and (-2y),
3x and x
In the second expression, the like terms are;
-y and -2y
3x and 4x
The first expression simplifies to 8y + 4x + 10
The second expression simplifies to 7x - 3y + 6
Question 4:
The expression is evaluated as 122
Question 5:
The equivalent expression of the expression 3(4x + 2y) + 5x, is 17x + 6y
To prove when x = 1 and y = 2 we have;
3(4×1 + 2×2) + 5×1 is 29
17×1 + 6×2 is 29 which are equivalent in value
Explanation:
Question 1:
The letter x or any letter used when writing an expression is representative of unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea
Example;
If x is the symbol representing the average number of oranges sold in 1 hour, then the expression for the number of oranges sold per day of 24 hours = 24·x
An expression is a written mathematical symbolic statement that shows the the finite merging together of representative symbols by the mathematical operations that govern the present constraints
An equation is a statement that two expressions are equal
Question 2:
The given expression is 2(3x - 2y) + 7
The parts are;
The coefficient of (3x - 2y) = 2
The constant term = 7
The variables are x and y
Which gives
The coefficient of the variable x = 6
The coefficient of the variable y = -4
The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7
or
The expression can be translated as two times the bracket open three times (variable) x minus two times (variable) y bracket close plus the constant 7
or
The expression can be expanded as 2(3x - 2y) + 7 → 6·x - 4·y + 7 which is expressed verbally as follows;
Six times (variable) x minus four times (variable) y plus the constant 7
Question 3:
The expressions are;
10y + 3x + 10 + x - 2y..........................(1)
3x - y + 4x + 6 - 2y,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2)
In the first expression, the like terms are;
10y and (-2y),
3x and x
In the second expression, the like terms are;
-y and -2y
3x and 4x
They are like terms because they can be simply added together to simplify the expressions as follows
10y + 3x + 10 + x - 2y gives 10y - 2y + 3x + x 10 to give 8y + 4x + 10
Also
3x - y + 4x + 6 - 2y gives 3x+ 4x - y - 2y + 6 to give 7x - 3y + 6
Question 4:
The expression 8x² + 25·y when x = 3 and y = 2 is evaluated by replacing (putting) the value x and y (into the expression)
The expression is then evaluated as 8×3² + 25×2 which is the same as 72 + 50 or 122
Question 5:
To write the equivalent expression of the expression 3(4x + 2y) + 5x, we expand the expression as follows;
3×4x + 3×2y + 4x which is 12x + 6y + 4x
We combine like terms;
12x + 5x + 6y which is 17x + 6y
To prove we can check by substituting a value for each of the variables x and y such as x = 1 and y = 2
3(4×1 + 2×2) + 5×1 is 29
17×1 + 6×2 is 29