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Question Find the value of nn in the equation 10n3−1.5=14.5\frac{10 n}{3} - 1.5 = 14.5. Give the answer as a decimal.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 10n3−1.5=14.5\frac{10n}{3} - 1.5 = 14.5.
2. We need to solve for the variable nn.
3. The solution for nn should be in decimal form.

STEP 2

First, we want to isolate the term containing nn on one side of the equation. To do this, we will add 1.5 to both sides of the equation to cancel out the -1.5 on the left side.
10n3−1.5+1.5=14.5+1.5\frac{10n}{3} - 1.5 + 1.5 = 14.5 + 1.5

STEP 3

Perform the addition on both sides of the equation.
10n3=16\frac{10n}{3} = 16

STEP 4

Now, we want to solve for nn. To do this, we will multiply both sides of the equation by 3 to cancel out the denominator of the fraction on the left side.
3×10n3=16×33 \times \frac{10n}{3} = 16 \times 3

STEP 5

Perform the multiplication on both sides of the equation.
10n=4810n = 48

STEP 6

To solve for nn, we will now divide both sides of the equation by 10 to isolate nn.
10n10=4810\frac{10n}{10} = \frac{48}{10}

STEP 7

Perform the division to find the value of nn.
n=4.8n = 4.8
The value of nn in the equation is 4.8.

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