Practice and master algebra concepts with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.
By Debi DalPezzo
Solving equations for an unknown
Why is this concept useful?
Where does this concept fit into the curriculum?
How can we use the concept:
Solving an equation is to find the value or values of the variable that makes it a true statement. Any value of the variable that makes the equation true is called a solution to the equation.
1) Solve each equation.
6(x – 4) + 5 = 11
Solution:
Step 1: To get rid of the parenthesis, use the distributive property: 6x - 24 + 5 = 11
Step 2: Combine Like terms: 6x - 19 = 11
Step 3: Use inverse Operations to isolate the x: add 19 to both sides of the equal sign 6x = 30
Then divide by 6, x = 5
2) Write the equation then solve.
The length of a rectangle is 11 cm more than the width. The perimeter is 90 cm. Find the length, the width, and the area.
Let x = width
x + 11 = length
Perimeter = x + x + x + 11 + x + 11 = 90
4x + 22 = 90
4x = 68
x = 17
Therefore the width of the rectangle is 17 cm and the length is 28 cm.
The area is 17 x 28 = 476
3) Write the equation then solve.
Find three consecutive odd integers whose sum is 105.
Let x = first odd integer
x + 2 = second odd integer
x + 4 = third odd integer
3x + 6 = 105
3x = 99
x = 33
The integers are 33, 35, and 37.
4) Six less than two-thirds of a number is 18. Find the number.
Take advantage of our free downloadable resources and study materials for at-home learning.
One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.
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Get PDF1. Solve for x.
x - (12 - x) = 38
2. Jim has $140 saved. He needs $200 for a new bike. If he saves $2.50 per week, after how many weeks will he have enough money to buy the new bike? Write and solve an equation.
3. The length of a rectangle is 7 in more than the width. The perimeter is 78 in. Find the length, width, and the area of the rectangle.
4. The sum of five consecutive integers is 195. Find the largest integer.