Put the steps in order to solve the equation: 3n+9+4n=2
. Put the reasoning in the first blank and the simplified equation in the second blank.
1. Combine like terms: We have 3n and 4n as like terms, so when we add them together, we get 7n. The equation becomes 7n + 9 = 2.
2. Subtract 9 from both sides: To isolate the variable, we need to get rid of the constant term 9. By subtracting 9 from both sides of the equation, we have 7n = 2 - 9, which simplifies to 7n = -7.
3. Divide both sides by 7: To solve for n, we need to get rid of the coefficient 7 that is multiplied with n. By dividing both sides of the equation by 7, we obtain n = -7/7, which simplifies to n = -1.
Therefore, the steps to solve the equation 3n + 9 + 4n = 2 are:
1. Combine like terms: 3n + 4n = 7n. The equation becomes 7n + 9 = 2.
2. Subtract 9 from both sides: 7n + 9 - 9 = 2 - 9. The equation simplifies to 7n = -7.
3. Divide both sides by 7: 7n/7 = -7/7. The equation simplifies to n = -1.
The base of a triangle is 4 less than three times the height. The area of the triangle is 38 square cm. A=b × h
An expression for the base of the triangle:. Response area
Equation for the area of the triangle: Response area
The first step in solving for h:
Step 1: Collect like terms by combining the coefficients of n.
Reasoning: We need to simplify the equation by adding the coefficients of n together.
Simplified equation: 3n + 4n + 9 = 2
Step 2: Combine the coefficients of n.
Reasoning: By adding the coefficients together, we can simplify the equation further.
Simplified equation: 7n + 9 = 2
Step 3: Subtract 9 from both sides of the equation.
Reasoning: We want to isolate the variable term by moving the constant term to the other side of the equation.
Simplified equation: 7n + 9 - 9 = 2 - 9
Step 4: Simplify both sides of the equation.
Reasoning: By performing the subtraction, we simplify the equation further.
Simplified equation: 7n = -7
Step 5: Divide both sides of the equation by 7.
Reasoning: We want to solve for n, so we need to isolate the variable by dividing both sides of the equation by the coefficient of n.
Simplified equation: (7n)/7 = -7/7
Step 6: Simplify both sides of the equation.
Reasoning: By performing the division, we simplify the equation further.
Simplified equation: n = -1
Final solution: The value of n that satisfies the equation 3n + 9 + 4n = 2 is n = -1.
To solve the equation 3n + 9 + 4n = 2, we want to isolate the variable "n" on one side of the equation. Here are the steps to do that:
1. Start with the given equation: 3n + 9 + 4n = 2
2. Combine like terms: Combine the 3n and 4n terms on the left side to simplify the equation. This gives us 7n + 9 = 2.
3. Get rid of the constant term: Subtract 9 from both sides of the equation to isolate the variable. This results in 7n = -7.
4. Divide by the coefficient of "n": Divide both sides of the equation by 7 to solve for "n". The equation becomes n = -1.
Reasoning: The reasoning behind these steps is to simplify the equation by combining like terms and then manipulate it algebraically to solve for "n". By performing each step logically and consistently, we can isolate the variable and find its value.
Simplified equation: The simplified equation after combining like terms is 7n + 9 = 2.