try to answer without solving the given equation: creating equivalent equations
1) if 5x + 14 = 10, what is the value of 5x + 17?
2) if 3x + 4 = 16, what is the value of 3x - 5?
3) if 12x + 6 = 5x - 3, what is the value of 7x + 6?
4) if 5x + 7 = 1, what is the value of 5x?
5) if 16x + 3 = 15x + 10, what is the value of x?
6) if 4x + 2 = 10, what is the value of 12x + 6?
challenge #1) if 3x - 8 = -21, what is the value of 6x - 7?
challenge #2) if ( x^3 + 7 = 21 ), what is the value of ( x^3 + 3 )?
challenge #3) if ( a + b = -2 ), what is the value of ( (a + b)^3 )?

Question

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Analyze the original equation
We have $ 5x + 14 = 10 $. We want to find $ 5x + 17 $. Notice that $ 5x + 17=(5x + 14)+3 $.
## Step2: Substitute the value from the original equation
From $ 5x + 14 = 10 $, substitute into the expression for $ 5x + 17 $. So $ 5x + 17=10 + 3=13 $.
# Answer:
$ 13 $

### Problem 2:
# Explanation:
## Step1: Analyze the original equation
We have $ 3x + 4 = 16 $. We want to find $ 3x-5 $. First, find $ 3x $ from the original equation. Subtract 4 from both sides of $ 3x + 4 = 16 $, we get $ 3x=16 - 4 = 12 $.
## Step2: Calculate the value of $ 3x-5 $
Now substitute $ 3x = 12 $ into $ 3x-5 $. So $ 3x-5=12-5 = 7 $.
# Answer:
$ 7 $

### Problem 3:
# Explanation:
## Step1: Analyze the original equation
We have $ 12x+6 = 5x - 3 $. We want to find $ 7x + 6 $. Subtract $ 5x $ from both sides of the original equation: $ 12x-5x+6=5x - 5x-3 $, which simplifies to $ 7x+6=-3 $.
# Answer:
$ -3 $

### Problem 4:
# Explanation:
## Step1: Analyze the original equation
We have $ 5x + 7 = 1 $. We want to find $ 5x $. Subtract 7 from both sides of the equation $ 5x+7 = 1 $.
## Step2: Calculate the value of $ 5x $
$ 5x=1 - 7=-6 $.
# Answer:
$ -6 $

### Problem 5:
# Explanation:
## Step1: Analyze the original equation
We have $ 16x + 3 = 15x+10 $. We want to find $ x $. Subtract $ 15x $ from both sides: $ 16x-15x + 3=15x-15x+10 $, which simplifies to $ x + 3=10 $.
## Step2: Solve for $ x $
Subtract 3 from both sides: $ x=10 - 3 = 7 $.
# Answer:
$ 7 $

### Problem 6:
# Explanation:
## Step1: Analyze the original equation
We have $ 4x + 2 = 10 $. We want to find $ 12x + 6 $. Notice that $ 12x + 6 = 3(4x + 2) $.
## Step2: Substitute the value from the original equation
From $ 4x + 2 = 10 $, substitute into $ 3(4x + 2) $. So $ 12x + 6=3\times10 = 30 $.
# Answer:
$ 30 $

### Challenge #1:
# Explanation:
## Step1: Analyze the original equation
We have $ 3x-8=-21 $. We want to find $ 6x - 7 $. First, multiply the original equation by 2: $ 2(3x - 8)=2\times(-21) $, which gives $ 6x-16=-42 $.
## Step2: Calculate the value of $ 6x - 7 $
We know that $ 6x-7=(6x - 16)+9 $. Substitute $ 6x - 16=-42 $ into it: $ 6x-7=-42 + 9=-33 $.
# Answer:
$ -33 $

### Challenge #2:
# Explanation:
## Step1: Analyze the original equation
We have $ x^{3}+7 = 21 $. We want to find $ x^{3}+3 $. Notice that $ x^{3}+3=(x^{3}+7)-4 $.
## Step2: Substitute the value from the original equation
From $ x^{3}+7 = 21 $, substitute into $ (x^{3}+7)-4 $. So $ x^{3}+3=21 - 4 = 17 $.
# Answer:
$ 17 $

### Challenge #3:
# Explanation:
## Step1: Analyze the original equation
We have $ a + b=-2 $. We want to find $ (a + b)^{3} $.
## Step2: Substitute the value of $ a + b $
Substitute $ a + b=-2 $ into $ (a + b)^{3} $. So $ (-2)^{3}=-8 $.
# Answer:
$ -8 $

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Analyze the original equation

Step2: Substitute the value from the original equation

Step1: Analyze the original equation

Step2: Calculate the value of \( 3x-5 \)

Step1: Analyze the original equation

Answer:

Problem 2: