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.(6 points)
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Step 1: Response area to get Response area
Step 2: Response area to get Response area
Step 3: Response area to get Response area
Step 1: Combine like terms on the left side of the equation. So, 3n + 4n simplifies to 7n. Therefore, the simplified equation is 7n + 9 = 2.
Step 2: Subtract 9 from both sides of the equation to isolate the variable term. This gives us 7n = -7.
Step 3: Divide both sides of the equation by 7 to solve for n. This yields 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 × h2
(3 points)
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An expression for the base of the triangle:
Equation for the area of the triangle:
The first step in solving for h:
An expression for the base of the triangle: 3h - 4
Equation for the area of the triangle: (3h - 4) * h / 2 = 38
The first step in solving for h: Simplify the equation by multiplying both sides by 2.
Match the equation with its solution.(3 points)
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3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5
3i+2i-4=18i --> Solution: i = -1
3(2i-7)=6i-21 --> Solution: i = 0
2i+3=2i-5 --> Solution: There is no solution.
Step 1: Combine like terms on the left side of the equation.
Reasoning: We have two terms with the variable n on the left side - 3n and 4n. We can add these terms together to simplify the expression.
Simplified equation: 7n + 9 = 2
Step 2: Move the constant term to the right side of the equation.
Reasoning: We want to isolate the variable n on one side of the equation. By moving the constant term 9 to the right side, we can do that.
Simplified equation: 7n = 2 - 9
Step 3: Simplify the right side of the equation.
Reasoning: We can simplify the expression on the right side by subtracting 9 from 2.
Simplified equation: 7n = -7
Step 1: Combine like terms on the left side of the equation using the distributive property. (Reasoning)
We have 3n + 4n which gives us a total of 7n. So the simplified equation becomes 7n + 9 = 2.
Step 2: Move the constant term (9) to the right side of the equation by subtracting it from both sides. (Reasoning)
Subtract 9 from both sides of the equation: 7n + 9 - 9 = 2 - 9. This simplifies to 7n = -7.
Step 3: Divide both sides of the equation by the coefficient of n (7) to solve for n. (Reasoning)
Divide both sides of the equation by 7: 7n/7 = -7/7. This simplifies to n = -1.
The final simplified equation after following these steps is n = -1.