Step 1: Subtract 7 from both sides of the equation: 8x = -33 - 7.
Justification: Subtracting 7 from both sides maintains the equality of the equation.
Step 2: Simplify the right side of the equation: 8x = -40.
Justification: The sum of -33 and -7 is -40.
Step 3: Divide both sides of the equation by 8: (8x)/8 = (-40)/8.
Justification: Dividing both sides by 8 maintains the equality of the equation.
Step 4: Simplify both sides of the equation: x = -5.
Justification: Dividing -40 by 8 results in -5.
Therefore, the solution to the equation 7 + 8x = -33 is x = -5.
Write the steps in solving 7+8x=−33 . Justify each step with an appropriate property.
7 answers
Is there an easier way to solve this equation?
Yes, an easier and quicker way to solve the equation 7 + 8x = -33 is by using the inverse operations. Here's the simplified process:
Step 1: Begin with the given equation 7 + 8x = -33.
Step 2: Subtract 7 from both sides to isolate the term with the variable: 8x = -33 - 7. Simplify to get 8x = -40.
Step 3: Divide both sides by 8 to solve for x: (8x)/8 = (-40)/8. Simplify to get x = -5.
Therefore, the solution to the equation is x = -5.
Step 1: Begin with the given equation 7 + 8x = -33.
Step 2: Subtract 7 from both sides to isolate the term with the variable: 8x = -33 - 7. Simplify to get 8x = -40.
Step 3: Divide both sides by 8 to solve for x: (8x)/8 = (-40)/8. Simplify to get x = -5.
Therefore, the solution to the equation is x = -5.
Write the steps in solving%C2%A06n−4+5n=73. %C2%A0 Justify each step with an appropriate property.
Step 1: Combine like terms on the left side of the equation to simplify: 6n + 5n - 4 = 73.
Justification: The property used here is the commutative property of addition, which allows us to rearrange the terms without changing the sum.
Step 2: Add the coefficients of the like terms: 11n - 4 = 73.
Justification: Combining the coefficients of the like terms gives us the simplified equation.
Step 3: Add 4 to both sides of the equation: 11n - 4 + 4 = 73 + 4.
Justification: Adding 4 to both sides maintains the equality of the equation.
Step 4: Simplify both sides of the equation: 11n = 77.
Justification: The sum of -4 and +4 is 0, so it cancels out on the left side. The sum of 73 and 4 is 77 on the right side.
Step 5: Divide both sides of the equation by 11 to solve for n: (11n)/11 = (77)/11.
Justification: Dividing both sides by 11 maintains the equality of the equation.
Step 6: Simplify both sides of the equation: n = 7.
Justification: Dividing 77 by 11 gives us the solution, which is n = 7.
Therefore, the solution to the equation 6n - 4 + 5n = 73 is n = 7.
Justification: The property used here is the commutative property of addition, which allows us to rearrange the terms without changing the sum.
Step 2: Add the coefficients of the like terms: 11n - 4 = 73.
Justification: Combining the coefficients of the like terms gives us the simplified equation.
Step 3: Add 4 to both sides of the equation: 11n - 4 + 4 = 73 + 4.
Justification: Adding 4 to both sides maintains the equality of the equation.
Step 4: Simplify both sides of the equation: 11n = 77.
Justification: The sum of -4 and +4 is 0, so it cancels out on the left side. The sum of 73 and 4 is 77 on the right side.
Step 5: Divide both sides of the equation by 11 to solve for n: (11n)/11 = (77)/11.
Justification: Dividing both sides by 11 maintains the equality of the equation.
Step 6: Simplify both sides of the equation: n = 7.
Justification: Dividing 77 by 11 gives us the solution, which is n = 7.
Therefore, the solution to the equation 6n - 4 + 5n = 73 is n = 7.
Is there a easier way to solve this?
Yes, there is an easier way to solve the equation 6n - 4 + 5n = 73 by combining like terms and isolating the variable. Here's the simplified process:
Step 1: Combine like terms on the left side of the equation: 6n + 5n - 4 = 73.
Simplify to get: 11n - 4 = 73.
Step 2: Add 4 to both sides of the equation to isolate the term with the variable: 11n - 4 + 4 = 73 + 4.
Simplify to get: 11n = 77.
Step 3: Divide both sides of the equation by 11 to solve for n: (11n)/11 = (77)/11.
Simplify to get: n = 7.
Therefore, the solution to the equation is n = 7.
By following this simplified method, we avoid justifying each step with properties and directly arrive at the solution.
Step 1: Combine like terms on the left side of the equation: 6n + 5n - 4 = 73.
Simplify to get: 11n - 4 = 73.
Step 2: Add 4 to both sides of the equation to isolate the term with the variable: 11n - 4 + 4 = 73 + 4.
Simplify to get: 11n = 77.
Step 3: Divide both sides of the equation by 11 to solve for n: (11n)/11 = (77)/11.
Simplify to get: n = 7.
Therefore, the solution to the equation is n = 7.
By following this simplified method, we avoid justifying each step with properties and directly arrive at the solution.
1 answer