Which of the following is equivalent to [tex]$8(2x - 5) - 4(3x - 7) = 7$[/tex]?

A. [tex]$16x - 40 - 12x + 28 = 7$[/tex]
B. [tex][tex]$16x - 5 - 12x - 7 = 7$[/tex][/tex]
C. [tex]$16x - 40 - 12x - 28 = 7$[/tex]
D. [tex]$16x - 5 + 12 - 7 = 7$[/tex]



Answer :

Let's solve the given equation step-by-step to determine which expression is equivalent to [tex]\( 8(2x - 5) - 4(3x - 7) = 7 \)[/tex].

First, we need to distribute the numbers outside the parentheses through each term inside the parentheses.

### Step 1: Distribute the 8 in [tex]\( 8(2x - 5) \)[/tex]
[tex]\[ 8(2x - 5) = 8 \cdot 2x - 8 \cdot 5 = 16x - 40 \][/tex]

### Step 2: Distribute the -4 in [tex]\( -4(3x - 7) \)[/tex]
[tex]\[ -4(3x - 7) = -4 \cdot 3x + 4 \cdot 7 = -12x + 28 \][/tex]

### Step 3: Combine the results from both distributions
[tex]\[ 8(2x - 5) - 4(3x - 7) = 16x - 40 - 12x + 28 \][/tex]

### Step 4: Simplify the combined expression
Combine like terms:
[tex]\[ (16x - 12x) + (-40 + 28) = 4x - 12 \][/tex]

So, the simplified form of the left-hand side of the equation is [tex]\( 4x - 12 \)[/tex]. Setting this equal to the right-hand side, we get:
[tex]\[ 4x - 12 = 7 \][/tex]

### Conclusion
Given these steps, let's see which of the provided options matches the equivalent expression:
1. [tex]\( 16x - 40 - 12x + 28 = 7 \)[/tex]
2. [tex]\( 16x - 5 - 12x - 7 = 7 \)[/tex]
3. [tex]\( 16x - 40 - 12x - 28 = 7 \)[/tex]
4. [tex]\( 16x - 5 + 12 - 7 = 7 \)[/tex]

From our steps, the correct equivalent expression is:
[tex]\[ 16x - 40 - 12x + 28 = 7 \][/tex]

Hence, the equivalent expression to [tex]\( 8(2x - 5) - 4(3x - 7) = 7 \)[/tex] is:
[tex]\[ 16x - 40 - 12x + 28 = 7 \][/tex]