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Math  /  Algebra

Question23x+14=10\frac{2}{3} x+14=10

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx that makes the equation 23x+14=10\frac{2}{3} x + 14 = 10 true! Watch out! Don't forget to keep track of the signs when moving terms around, and be careful when multiplying or dividing by fractions.

STEP 2

1. Isolate the term with xx.
2. Isolate xx.

STEP 3

We want to get the term with xx by itself, so let's **subtract 14** from both sides of the equation.
Remember, what we do to one side, we *must* do to the other! 23x+14−14=10−14 \frac{2}{3}x + 14 - 14 = 10 - 14 23x=−4 \frac{2}{3}x = -4 Now we have 23x\frac{2}{3}x all alone on one side!

STEP 4

To completely isolate xx, we need to multiply both sides of the equation by the **reciprocal** of 23\frac{2}{3}, which is 32\frac{3}{2}.
Multiplying a fraction by its reciprocal gives us **one**, and one times anything is itself! 32⋅23x=−4⋅32 \frac{3}{2} \cdot \frac{2}{3}x = -4 \cdot \frac{3}{2} 3⋅22⋅3x=−4⋅32 \frac{3 \cdot 2}{2 \cdot 3}x = \frac{-4 \cdot 3}{2}

STEP 5

Let's simplify the left side.
Notice that we can divide the numerator and denominator by **2**, and also by **3**. 3⋅22⋅3x=1⋅11⋅1x=1⋅x=x \frac{3 \cdot 2}{2 \cdot 3}x = \frac{1 \cdot 1}{1 \cdot 1}x = 1 \cdot x = x Now, let's simplify the right side.
We can divide both −4-4 and 22 by **2**. −4⋅32=−2⋅31=−6 \frac{-4 \cdot 3}{2} = \frac{-2 \cdot 3}{1} = -6

STEP 6

Putting it all together, we get: x=−6 x = -6 Woohoo! We found xx!

STEP 7

The value of xx that satisfies the equation is x=−6x = -6.

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