7th Grade Algebra Problems

Introduction to algebra practice exercises:

Algebra is One of the subdivision in mathematics that is related with variables and numbers, it also revise rules of operations and relationships, and the concepts arising from them. Including polynomials, terms, algebraic structures and equations, along with analysis, topology, geometry, and number theory. Algebra is one of the ultimate branches of mathematics Here it is about the algebra problem exercise with the problems and solution.

Examples from Algebra Practice Exercises

Algebra practice exercises - Problem 1:

Two consecutive numbers have a sum of 81. What are the numbers?

Sol :

To begin solving this problem, define the variable in algebraic form. You do not know what the first consecutive number  is, so you can call it x.
Let x = The First Consecutive Number
Since the numbers are having consecutive value,one number comes one after the other, the second number must be one more than the first. So, x + 1 equals the second number.
Let x + 1 = The Second Consecutive Number
The problem says that the sum of the two numbers gives the value 81. This can be shown in the equation like the following:
x + (x + 1) = 81
The equation that can be just wrote can be solved as follows:
Initial Equation
x + (x + 1) = 81
After combining like terms
2x + 1 = 81
After subtracting 1 from each side
2x = 80
After dividing each side by 2
x = 40

Answer : x = 40

Algebra practice exercises - Problem 2:

12x + 2y = 20 (equation 1)
y + 8 = 12x (equation 2)

Sol:

Step 1:
To choose the equation in which the coefficient of the variable is 1.
Choose equation 2 to isolate the variable y
y = 12x – 8 (equation 3)

Step 2:
From equation 3, we know that the y-value is same as the equation 12x – 8
We can  substitute the variable for y-values in the equation 1 with the equation 12x – 8
12x + 2 (12x – 8) = 20

Step 3:
Remove the brackets by using the distributive property
12x + 24x – 16 = 20

Step 4:
To combine the terms
36x – 16 = 20

Step 5:
To Isolate the variable of x
36x = 36
x = 36/36
x = 1

Step 6:
Substitute x = 1 in the equation 3 to get the y-value.
y = 12(1) – 8
y = 12– 8 = 4

Step 7:
To check the answer with the equation 1
12 (1) + 2 (4) = 12 +8 = 20

Answer:
x = 1 and y = 4

Algebra practice exercises - Problem 3:

Sol:

Given the algebraic expression

2(a -3) + 4b - 2(a -b -3) + 5

Multiply factors.

= 2a - 6 + 4b -2a + 2b + 6 + 5

Group like terms.

= 6b + 5


Practice Exercise Questions from Algebra

Problem 1:  Solve           10x +4y = 22

y+10 = 16x
Answer: x = `(31/36) ` and y= `(124/9)`
Problem 2:
Given the algebraic expression
5(a -2) + 3b - 3(a -b -2) + 6
Answer: 2a - 10
Problem 3:
Exapnd (2x + 3y +4z)2
Answer: 4x2+9y2+16Z2+12xy+24yz+16zx
Problem 4:
Expand (3a + 2b -3c)2
Answer: 9a2 +4b2 +9c2 +12ab - 12bc - 18ca
Problem 5:
If a2+b2+c2 = 80 and ab + bc+ ca = 32, find the value of a+b+c.
Answer: 12