Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 20, 2024

Solve the linear equation $p - 5 = \frac{7}{2}(t - 4)$ for the variable $p$ .

STEP 1

Assumptions
1. We are given the equation $p - 5 = \frac{7}{2}(t - 4)$ .
2. We need to solve for $p$ in terms of $t$ .

STEP 2

First, we will distribute the fraction $\frac{7}{2}$ across the terms inside the parentheses on the right side of the equation.
$p - 5 = \frac{7}{2}t - \frac{7}{2} \cdot 4$

STEP 3

Multiply $\frac{7}{2}$ by 4 to simplify the right side of the equation.
$p - 5 = \frac{7}{2}t - 14$

STEP 4

Now, we will isolate $p$ on the left side of the equation by adding 5 to both sides.
$p = \frac{7}{2}t - 14 + 5$

STEP 5

Combine the constants on the right side of the equation.
$p = \frac{7}{2}t - 9$
This is the solution for $p$ in terms of $t$ .

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