Solved on Jan 17, 2024

Find the value of $n$ in the equation $4n-3=5$ by drawing a flowchart and using backtracking. (4 marks)

STEP 1

Assumptions
1. The equation to solve is $4n - 3 = 5$ .
2. We will use algebraic manipulation to isolate $n$ and solve for its value.
3. Backtracking involves reversing the operations applied to $n$ to solve the equation.

STEP 2

The first step in solving the equation is to isolate the term containing $n$ on one side. We start by adding 3 to both sides of the equation to cancel out the -3.
$4n - 3 + 3 = 5 + 3$

STEP 3

Simplify both sides of the equation.
$4n = 8$

STEP 4

Now, we need to isolate $n$ by dividing both sides of the equation by 4.
$\frac{4n}{4} = \frac{8}{4}$

STEP 5

Simplify the equation to find the value of $n$ .
$n = 2$

STEP 6

To backtrack, we reverse the operations starting from the solution $n = 2$ . First, we multiply $n$ by 4.
$4 \cdot n = 4 \cdot 2$

STEP 7

Simplify the multiplication to confirm the intermediate step.
$4n = 8$

STEP 8

Next, we add 3 to the result of $4n$ to confirm that we get the original equation.
$4n + 3 = 8 + 3$

STEP 9

Simplify the addition to confirm the original equation.
$4n + 3 = 11$

STEP 10

We notice that the result $4n + 3 = 11$ does not match the original equation $4n - 3 = 5$ . This indicates an error in our backtracking process. We should have subtracted 3, not added 3, to backtrack correctly. Let's correct this in the next step.

STEP 11

To backtrack correctly, we subtract 3 from the result of $4n$ to match the original equation.
$4n - 3 = 8 - 3$

STEP 12

Simplify the subtraction to confirm the original equation.
$4n - 3 = 5$

STEP 13

Now we have confirmed that the original equation $4n - 3 = 5$ is satisfied when $n = 2$ . This completes the backtracking process and confirms that $n = 2$ is the correct solution to the equation.
The value of $n$ is 2.

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Find the value of $n$ in the equation $4n-3=5$ by drawing a flowchart and using backtracking. (4 marks)

STEP 1

Assumptions
1. The equation to solve is $4n - 3 = 5$ .
2. We will use algebraic manipulation to isolate $n$ and solve for its value.
3. Backtracking involves reversing the operations applied to $n$ to solve the equation.

STEP 2

The first step in solving the equation is to isolate the term containing $n$ on one side. We start by adding 3 to both sides of the equation to cancel out the -3.
$4n - 3 + 3 = 5 + 3$

STEP 3

Simplify both sides of the equation.
$4n = 8$

STEP 4

Now, we need to isolate $n$ by dividing both sides of the equation by 4.
$\frac{4n}{4} = \frac{8}{4}$

STEP 5

Simplify the equation to find the value of $n$ .
$n = 2$

STEP 6

To backtrack, we reverse the operations starting from the solution $n = 2$ . First, we multiply $n$ by 4.
$4 \cdot n = 4 \cdot 2$

STEP 7

Simplify the multiplication to confirm the intermediate step.
$4n = 8$

STEP 8

Next, we add 3 to the result of $4n$ to confirm that we get the original equation.
$4n + 3 = 8 + 3$

STEP 9

Simplify the addition to confirm the original equation.
$4n + 3 = 11$

STEP 10

We notice that the result $4n + 3 = 11$ does not match the original equation $4n - 3 = 5$ . This indicates an error in our backtracking process. We should have subtracted 3, not added 3, to backtrack correctly. Let's correct this in the next step.

STEP 11

To backtrack correctly, we subtract 3 from the result of $4n$ to match the original equation.
$4n - 3 = 8 - 3$

STEP 12

Simplify the subtraction to confirm the original equation.
$4n - 3 = 5$

STEP 13

Now we have confirmed that the original equation $4n - 3 = 5$ is satisfied when $n = 2$ . This completes the backtracking process and confirms that $n = 2$ is the correct solution to the equation.
The value of $n$ is 2.

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Find the value of nnn in the equation 4n−3=54n-3=54n−3=5 by drawing a flowchart and using backtracking. (4 marks)

STEP 1

Assumptions1. The equation to solve is 4n−3=54n - 3 = 54n−3=5.2. We will use algebraic manipulation to isolate nnn and solve for its value.3. Backtracking involves reversing the operations applied to nnn to solve the equation.

STEP 2

The first step in solving the equation is to isolate the term containing nnn on one side. We start by adding 3 to both sides of the equation to cancel out the -3.4n−3+3=5+34n - 3 + 3 = 5 + 34n−3+3=5+3

STEP 3

Simplify both sides of the equation.4n=84n = 84n=8

STEP 4

Now, we need to isolate nnn by dividing both sides of the equation by 4.4n4=84\frac{4n}{4} = \frac{8}{4}44n​=48​

STEP 5

Simplify the equation to find the value of nnn.n=2n = 2n=2

STEP 6

To backtrack, we reverse the operations starting from the solution n=2n = 2n=2. First, we multiply nnn by 4.4⋅n=4⋅24 \cdot n = 4 \cdot 24⋅n=4⋅2

STEP 7

Simplify the multiplication to confirm the intermediate step.4n=84n = 84n=8

STEP 8

Next, we add 3 to the result of 4n4n4n to confirm that we get the original equation.4n+3=8+34n + 3 = 8 + 34n+3=8+3

STEP 9

Simplify the addition to confirm the original equation.4n+3=114n + 3 = 114n+3=11

STEP 10

We notice that the result 4n+3=114n + 3 = 114n+3=11 does not match the original equation 4n−3=54n - 3 = 54n−3=5. This indicates an error in our backtracking process. We should have subtracted 3, not added 3, to backtrack correctly. Let's correct this in the next step.

STEP 11

To backtrack correctly, we subtract 3 from the result of 4n4n4n to match the original equation.4n−3=8−34n - 3 = 8 - 34n−3=8−3

STEP 12

Simplify the subtraction to confirm the original equation.4n−3=54n - 3 = 54n−3=5

STEP 13

Now we have confirmed that the original equation 4n−3=54n - 3 = 54n−3=5 is satisfied when n=2n = 2n=2. This completes the backtracking process and confirms that n=2n = 2n=2 is the correct solution to the equation.The value of nnn is 2.

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Find the value of $n$ in the equation $4n-3=5$ by drawing a flowchart and using backtracking. (4 marks)

Assumptions
1. The equation to solve is $4n - 3 = 5$ .
2. We will use algebraic manipulation to isolate $n$ and solve for its value.
3. Backtracking involves reversing the operations applied to $n$ to solve the equation.

The first step in solving the equation is to isolate the term containing $n$ on one side. We start by adding 3 to both sides of the equation to cancel out the -3.
$4n - 3 + 3 = 5 + 3$

Simplify both sides of the equation.
$4n = 8$

Now, we need to isolate $n$ by dividing both sides of the equation by 4.
$\frac{4n}{4} = \frac{8}{4}$

Simplify the equation to find the value of $n$ .
$n = 2$

To backtrack, we reverse the operations starting from the solution $n = 2$ . First, we multiply $n$ by 4.
$4 \cdot n = 4 \cdot 2$

Simplify the multiplication to confirm the intermediate step.
$4n = 8$

Next, we add 3 to the result of $4n$ to confirm that we get the original equation.
$4n + 3 = 8 + 3$

Simplify the addition to confirm the original equation.
$4n + 3 = 11$

We notice that the result $4n + 3 = 11$ does not match the original equation $4n - 3 = 5$ . This indicates an error in our backtracking process. We should have subtracted 3, not added 3, to backtrack correctly. Let's correct this in the next step.

To backtrack correctly, we subtract 3 from the result of $4n$ to match the original equation.
$4n - 3 = 8 - 3$

Simplify the subtraction to confirm the original equation.
$4n - 3 = 5$

Now we have confirmed that the original equation $4n - 3 = 5$ is satisfied when $n = 2$ . This completes the backtracking process and confirms that $n = 2$ is the correct solution to the equation.
The value of $n$ is 2.