Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Mar 01, 2024

Find the value(s) of $z$ that satisfy the equation $3=\frac{z+4}{3}$ .

STEP 1

Assumptions
1. We are given the equation $\frac{z+4}{3} = 3$ .
2. We need to solve for the variable $z$ .
3. The possible solutions provided are $z = -7$ and $z = 5$ .

STEP 2

To solve for $z$ , we need to isolate $z$ on one side of the equation. We can start by multiplying both sides of the equation by 3 to eliminate the denominator.
$3 \times \frac{z+4}{3} = 3 \times 3$

STEP 3

Now simplify both sides of the equation.
$z + 4 = 9$

STEP 4

Next, we subtract 4 from both sides of the equation to solve for $z$ .
$z + 4 - 4 = 9 - 4$

STEP 5

Simplify the equation to find the value of $z$ .
$z = 5$
The value of $z$ that satisfies the equation is $z = 5$ .

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