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MEAP Preparation - Grade 7 Mathematics
2.41 Solving Equations

Simplifying with Addition and Subtraction:
We can use addition and subtraction to get all the terms with variables on one side of an equation, and all the numeric terms on the other. The equations 3x = 17, 21 = y, and z/12 = 24 each have a variable term on one side of the '=' sign, and a number on the other. The equations x + 3 = 12, 21 = 30 - y, and (z + 2) 4 = 10 do not.
We usually do this after simplifying each side using the distributive rules, eliminating parentheses, and combining like terms. Since addition is associative, it can be helpful to add a negative number to each side instead of subtracting.

Examples:

  • For the equation 3x + 4 = 12, we can separate the variable term on the left by subtracting a 4 from both sides:
    3x + 4 - 4 = 12 - 4
    3x = 8.
    x = 8/3
  • For the equation 7y - 200 = 10, if we add 200 to both sides of the equation, the 200 and -200 will cancel each other on the left hand side:
    7y + (-200) + 200 = 10 + 200
    7y = 210
    y = 30

Example:
For the equation 8 = 20 - z, we can add z to both sides to get
8 + z = 20 - z + z
=> 8 + z = 20. Now subtracting 8 from both sides,
8 + z - 8 = 20 - 8
Therefore, z = 12

Simplifying by Multiplication
When solving for a variable, we want to get a solution like x = 3 or z = 198 etc. When a variable is divided by some number, we can use multiplication on both sides to solve for the variable.

Example:
Solve for x in the equation x 12 = 5.
Since the x on the left side is being divided by 12, the equation is the same as x 1/12 = 5.
Multiplying both sides by 12 will cancel the 1/12 on the left side:
x 1/12 12 = 5 12 ==>
x 1 = 60 ==>
x = 60.


Simplifying by Division
When solving for a variable, we want to get a solution like x = 9 or y = 21 etc. When a variable is multiplied by some number, we can use division on both sides to solve for the variable.
Example:
Solve for x in the equation 7x = 280. Since the x on the left side is being multiplied by 7, we can divide both sides by 7 to solve for x:
7x 7 = 280 7
(7x)/7 = 280 7
x/1 = 40
x = 40.
Note: Dividing by 7 is the same as multiplying both sides by 1/7.

Directions: Solve the following equations and enter the solution. Also write at least 10 examples of your own.
Q 1: Solve: f + 16 =100
Answer:

Q 2: Solve: n/7 = 8
Answer:

Q 3: Solve: x/7 =4
Answer:

Q 4: Solve: 5x =45
Answer:

Q 5: Solve: d + 16 = 64
Answer:

Q 6: Solve: x + 8 = 17
Answer:

Q 7: Solve: d - 12 =69
Answer:

Q 8: Solve: 7u = 35
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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