Math  /  Algebra

QuestionQuestion 9 (1 point) The sum of 5.5 and twice a number is -10 What is the number? n=2.125n=-2.125 n=2.125n=2.125 n=7.75n=7.75 n=7.75n=-7.75

Studdy Solution

STEP 1

What is this asking? We need to find a mystery number, and we know that if we double it and add 5.5, we get -10. Watch out! Be careful with negative numbers!
It's easy to make a mistake with signs.

STEP 2

1. Set up the equation
2. Isolate the term with the variable
3. Solve for the variable

STEP 3

Let's call our mystery number nn. "Twice a number" means 2n2 \cdot n. "The sum of 5.5 and twice a number" translates to 5.5+2n5.5 + 2 \cdot n.
This whole thing equals 10-10, so our equation is 5.5+2n=105.5 + 2 \cdot n = -10.

STEP 4

We want to get nn by itself.
First, let's get rid of that 5.5.
Since it's added to 2n2 \cdot n, we'll subtract it from *both* sides of the equation to keep things balanced.
This is like adding 5.5-5.5 to both sides, so that the 5.5 adds to zero on the left side.

STEP 5

5.5+2n+(5.5)=10+(5.5)5.5 + 2 \cdot n + (-5.5) = -10 + (-5.5) 2n=15.52 \cdot n = -15.5

STEP 6

Now, we have 2n=15.52 \cdot n = -15.5.
We want just one nn, not two of them!
Since nn is multiplied by 2, we'll divide *both* sides by **2**.
This is like multiplying both sides by 12 \frac{1}{2} so that the 2 multiplies to one on the left side.

STEP 7

2n2=15.52 \frac{2 \cdot n}{2} = \frac{-15.5}{2} n=7.75 n = -7.75

STEP 8

The mystery number nn is 7.75-7.75!

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