Question $5 x-(11+17)=4 x-12$ Equation $\# 2$ is will give you solution $8(x+4)=5 x+8$ quation \#3 This will give you solution \#2 $4(x+5)-3=6 x-13 \quad 6(x-9)=4(x-5)$

Studdy Solution

STEP 1

What is this asking? We've got three separate equations to solve for $x$ !
Let's find those $x$ values! Watch out! Don't forget to keep track of your signs and simplify carefully!
A little slip-up can lead to a wrong answer, so let's stay focused.

STEP 2

1. Solve Equation #1
2. Solve Equation #2
3. Solve Equation #3

STEP 3

Alright, let's kick things off with Equation #1: $5x - (11 + 17) = 4x - 12$ .
First, we simplify inside the parentheses: $11 + 17 = 28$ .
So, our equation becomes $5x - 28 = 4x - 12$ .

STEP 4

Now, let's group those $x$ terms.
We can subtract $4x$ from both sides: $5x - 4x - 28 = 4x - 4x - 12$ .
This simplifies to $x - 28 = -12$ .

STEP 5

Almost there!
Let's isolate $x$ by adding $28$ to both sides: $x - 28 + 28 = -12 + 28$ .
This gives us our solution: $x = 16$ !

STEP 6

Equation #2 is $8(x + 4) = 5x + 8$ .
Let's distribute that $8$ : $8 \cdot x + 8 \cdot 4 = 5x + 8$ , which simplifies to $8x + 32 = 5x + 8$ .

STEP 7

Time to group the $x$ terms again!
Subtract $5x$ from both sides: $8x - 5x + 32 = 5x - 5x + 8$ .
This simplifies to $3x + 32 = 8$ .

STEP 8

Let's isolate $x$ .
Subtract $32$ from both sides: $3x + 32 - 32 = 8 - 32$ , which gives us $3x = -24$ .

STEP 9

Finally, divide both sides by $3$ : $\frac{3x}{3} = \frac{-24}{3}$ .
This gives us our solution: $x = -8$ !

STEP 10

Equation #3 has two parts: $4(x + 5) - 3 = 6x - 13$ and $6(x - 9) = 4(x - 5)$ .
Let's tackle the first one. Distribute the $4$ : $4 \cdot x + 4 \cdot 5 - 3 = 6x - 13$ .
This simplifies to $4x + 20 - 3 = 6x - 13$ , and further to $4x + 17 = 6x - 13$ .

STEP 11

Subtract $4x$ from both sides: $4x - 4x + 17 = 6x - 4x - 13$ , which simplifies to $17 = 2x - 13$ .
Now, add $13$ to both sides: $17 + 13 = 2x - 13 + 13$ , giving us $30 = 2x$ .

STEP 12

Divide both sides by $2$ : $\frac{30}{2} = \frac{2x}{2}$ .
This gives us the solution $x = 15$ for the first part.

STEP 13

Now, for the second part: $6(x - 9) = 4(x - 5)$ . Distribute the $6$ and the $4$ : $6 \cdot x - 6 \cdot 9 = 4 \cdot x - 4 \cdot 5$ , simplifying to $6x - 54 = 4x - 20$ .

STEP 14

Subtract $4x$ from both sides: $6x - 4x - 54 = 4x - 4x - 20$ , simplifying to $2x - 54 = -20$ . Add $54$ to both sides: $2x - 54 + 54 = -20 + 54$ , giving us $2x = 34$ .

STEP 15

Finally, divide both sides by $2$ : $\frac{2x}{2} = \frac{34}{2}$ .
This gives us the solution $x = 17$ for the second part.

STEP 16

Equation #1: $x = 16$ Equation #2: $x = -8$ Equation #3 (part 1): $x = 15$ Equation #3 (part 2): $x = 17$

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