Select all the expressions equivalent to 15m5−3(42−13m)−10.
A:4(m−4)
B:4m−16
C:3(m−13)/5
D:3(m−10)/5
E:3m−12/5
impatient much?
Once is enough, thank you.
Repeated postings will not get faster or better responses.
and try to fix your math notation. It's clearly bogus.
well, well ...
15m/5−3(4/2−1/3 m)−10 = 4m-16
To find the equivalent expressions for 15m5−3(42−13m)−10, we can simplify the given expression step-by-step.
Step 1: Simplify the expression inside the parentheses:
42−13m = -13m + 42 = 42 - 13m
Step 2: Distribute the -3 to both terms inside the parentheses:
-3(42-13m) = -3 * 42 + (-3) * (-13m) = -126 + 39m
Step 3: Rewrite the expression with the simplified terms:
15m5−(-126+39m)−10 = 15m5 + 126 - 39m - 10
Step 4: Combine the like terms:
15m5 + 126 - 39m - 10 = 15m - 39m + 126 + 5 - 10 = -24m + 121
So, the equivalent expression for 15m5−3(42−13m)−10 is -24m + 121.
Now let's check each given option to see which ones are equivalent to -24m + 121:
A: 4(m−4) = 4m - 16
B: 4m−16
C: 3(m−13)/5 = 3m/5 - 39/5
D: 3(m−10)/5 = 3m/5 - 30/5 = 3m/5 - 6
E: 3m−12/5
From the above options, only option B: 4m−16 is equivalent to -24m + 121.
Therefore, the correct answer is B: 4m−16.
To determine which expressions are equivalent to 15m5−3(42−13m)−10, we must simplify the given expression by following the order of operations (PEMDAS/BODMAS).
Let's break down the process step by step:
1. Distribute the negative sign (-3) into the parentheses:
15m5−3(42−13m)−10 = 15m5−3 * 42 + 3 * 13m - 10
2. Multiply -3 by 42:
15m5−126 + 3 * 13m - 10 = 15m5−126 + 39m - 10
3. Combine like terms (the m terms):
15m5 + 39m−126−10 = 54m−136
Now that we have simplified the original expression to 54m−136, let's check each option to see which ones are equivalent:
A: 4(m−4) = 4m−16
B: 4m−16 (matches the simplified expression, 54m−136)
C: 3(m−13)/5 = 3m−39/5
D: 3(m−10)/5 = 3m−30/5 = 3m−6
E: 3m−12/5
Comparing the simplified expression (54m−136) to the given options, we find that option B (4m−16) is equivalent and matches the simplified expression. Therefore, option B is the correct answer.