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Answer :
Let's solve the problem step by step, focusing on simplifying the expression and finding its equivalent form.
We start with the given expression:
[tex]\[ 30\left(\frac{1}{2}x - 2\right) + 40\left(\frac{3}{4}y - 4\right) \][/tex]
Step 1: Distribute the constants inside the parentheses.
- For the first part, distribute 30:
- [tex]\( 30 \times \frac{1}{2}x = 15x \)[/tex]
- [tex]\( 30 \times -2 = -60 \)[/tex]
- For the second part, distribute 40:
- [tex]\( 40 \times \frac{3}{4}y = 30y \)[/tex]
- [tex]\( 40 \times -4 = -160 \)[/tex]
Step 2: Combine all the terms.
The expression translates to:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
Step 3: Simplify the expression.
Combine the constant terms:
- [tex]\(-60 - 160 = -220\)[/tex]
So, the simplified expression is:
[tex]\[ 15x + 30y - 220 \][/tex]
Therefore, the expression equivalent to the given one is:
[tex]\[ 15x + 30y - 220 \][/tex]
This matches with the option [tex]\( \boxed{15x + 30y - 220} \)[/tex].
We start with the given expression:
[tex]\[ 30\left(\frac{1}{2}x - 2\right) + 40\left(\frac{3}{4}y - 4\right) \][/tex]
Step 1: Distribute the constants inside the parentheses.
- For the first part, distribute 30:
- [tex]\( 30 \times \frac{1}{2}x = 15x \)[/tex]
- [tex]\( 30 \times -2 = -60 \)[/tex]
- For the second part, distribute 40:
- [tex]\( 40 \times \frac{3}{4}y = 30y \)[/tex]
- [tex]\( 40 \times -4 = -160 \)[/tex]
Step 2: Combine all the terms.
The expression translates to:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
Step 3: Simplify the expression.
Combine the constant terms:
- [tex]\(-60 - 160 = -220\)[/tex]
So, the simplified expression is:
[tex]\[ 15x + 30y - 220 \][/tex]
Therefore, the expression equivalent to the given one is:
[tex]\[ 15x + 30y - 220 \][/tex]
This matches with the option [tex]\( \boxed{15x + 30y - 220} \)[/tex].
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