Math  /  Algebra

Question4. x9=3\frac{x}{9}=3
5. 45z=16\frac{4}{5} z=16

Studdy Solution

STEP 1

What is this asking? We're asked to solve two simple equations for xx and zz.
Piece of cake! Watch out! Don't forget to double-check your work by plugging your answers back into the original equations.
It's a super easy way to catch any silly mistakes!

STEP 2

1. Solve for xx
2. Solve for zz

STEP 3

Alright, let's **tackle** the first equation: x9=3\frac{x}{9} = 3.
Our goal is to get xx all by itself.
It's currently being divided by **9**.
To undo this division, we'll **multiply both sides** of the equation by **9**.

STEP 4

x99=39 \frac{x}{9} \cdot 9 = 3 \cdot 9 Remember, multiplying by 99\frac{9}{9} is the same as multiplying by **1**, and multiplying anything by **1** doesn't change its value!

STEP 5

So, we get: x=27 x = \textbf{27}

STEP 6

Now, let's **conquer** the second equation: 45z=16\frac{4}{5}z = 16.
We want to **isolate** zz.
It's being multiplied by 45\frac{\textbf{4}}{\textbf{5}}.
To undo this, we'll multiply both sides by the **reciprocal**, which is 54\frac{\textbf{5}}{\textbf{4}}.

STEP 7

5445z=1654 \frac{5}{4} \cdot \frac{4}{5} z = 16 \cdot \frac{5}{4} Multiplying 45\frac{4}{5} by 54\frac{5}{4} gives us 2020\frac{20}{20}, which is just **1**!

STEP 8

z=1654 z = \frac{16 \cdot 5}{4}

STEP 9

z=804 z = \frac{80}{4}

STEP 10

z=20 z = \textbf{20}

STEP 11

We found x=27x = \textbf{27} and z=20z = \textbf{20}.
Boom!

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