Answer :
Sure! Let's go through the expression step-by-step to simplify it.
The expression given is:
[tex]\[ 30\left(\frac{1}{2}x - 2\right) + 40\left(\frac{3}{4}y - 4\right) \][/tex]
### Step 1: Distribute the 30 into the expression [tex]\(\left(\frac{1}{2}x - 2\right)\)[/tex]
Distribute 30 to both terms inside the parentheses:
[tex]\[ 30 \times \frac{1}{2}x = 15x \][/tex]
[tex]\[ 30 \times (-2) = -60 \][/tex]
So, the expression becomes:
[tex]\[ 15x - 60 \][/tex]
### Step 2: Distribute the 40 into the expression [tex]\(\left(\frac{3}{4}y - 4\right)\)[/tex]
Now, distribute 40 to both terms inside the parentheses:
[tex]\[ 40 \times \frac{3}{4}y = 30y \][/tex]
[tex]\[ 40 \times (-4) = -160 \][/tex]
So, the expression becomes:
[tex]\[ 30y - 160 \][/tex]
### Step 3: Combine all the terms from both distributed expressions
Combine the results from step 1 and step 2:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
### Step 4: Simplify the expression
Combine like terms:
The constant terms [tex]\(-60\)[/tex] and [tex]\(-160\)[/tex] can be simplified as:
[tex]\[ -60 - 160 = -220 \][/tex]
So, the final expression becomes:
[tex]\[ 15x + 30y - 220 \][/tex]
The expression simplifies to [tex]\(15x + 30y - 220\)[/tex].
Therefore, the equivalent expression is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]
This corresponds to the answer:
[tex]$15 x + 30 y - 220$[/tex]
The expression given is:
[tex]\[ 30\left(\frac{1}{2}x - 2\right) + 40\left(\frac{3}{4}y - 4\right) \][/tex]
### Step 1: Distribute the 30 into the expression [tex]\(\left(\frac{1}{2}x - 2\right)\)[/tex]
Distribute 30 to both terms inside the parentheses:
[tex]\[ 30 \times \frac{1}{2}x = 15x \][/tex]
[tex]\[ 30 \times (-2) = -60 \][/tex]
So, the expression becomes:
[tex]\[ 15x - 60 \][/tex]
### Step 2: Distribute the 40 into the expression [tex]\(\left(\frac{3}{4}y - 4\right)\)[/tex]
Now, distribute 40 to both terms inside the parentheses:
[tex]\[ 40 \times \frac{3}{4}y = 30y \][/tex]
[tex]\[ 40 \times (-4) = -160 \][/tex]
So, the expression becomes:
[tex]\[ 30y - 160 \][/tex]
### Step 3: Combine all the terms from both distributed expressions
Combine the results from step 1 and step 2:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
### Step 4: Simplify the expression
Combine like terms:
The constant terms [tex]\(-60\)[/tex] and [tex]\(-160\)[/tex] can be simplified as:
[tex]\[ -60 - 160 = -220 \][/tex]
So, the final expression becomes:
[tex]\[ 15x + 30y - 220 \][/tex]
The expression simplifies to [tex]\(15x + 30y - 220\)[/tex].
Therefore, the equivalent expression is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]
This corresponds to the answer:
[tex]$15 x + 30 y - 220$[/tex]