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Which equation is equivalent to the given equation?

[tex]\( 7m + 11 = -4(2m + 3) \)[/tex]

A. [tex]\(-m = 1\)[/tex]

B. [tex]\(15m = -23\)[/tex]

C. [tex]\(-m = -1\)[/tex]

D. [tex]\(-15m = -23\)[/tex]

Sagot :

GinnyAnswer
To determine which equation is equivalent to the given equation:
[tex]\[ 7m + 11 = -4(2m + 3) \][/tex]

we can follow these steps to simplify and solve the equation:

1. Distribute the [tex]\(-4\)[/tex] on the right side of the equation:
[tex]\[ 7m + 11 = -4 \cdot 2m - 4 \cdot 3 \][/tex]
This simplifies to:
[tex]\[ 7m + 11 = -8m - 12 \][/tex]

2. Move all terms involving [tex]\(m\)[/tex] to the left side and constant terms to the right side:
[tex]\[ 7m + 8m = -12 - 11 \][/tex]

3. Combine like terms:
[tex]\[ 15m = -23 \][/tex]

Thus, the simplified equation is:
[tex]\[ 15m = -23 \][/tex]

So the correct answer is:
[tex]\[ \boxed{15m = -23} \][/tex]

This matches option B.
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