Let m=2x+3. Which equation is equivalent to (2x+3)^(2)-14 x-21=-6 in terms of m ? Choose 1 answer: (A) m^(2)+7m+6=0 (B) m^(2)-7m-15=0 (c) m^(2)-7m+6=0 (D) m^(2)+7m-15=0

Substitute m into equation: We are given m = 2x + 3. Let's substitute m into the given equation (2x+3)^(2)-14x-21=-6 to find the equivalent equation in terms of m.Replace 14x with 7m: First, we substitute m into the equation: (m)^(2)-14x-21=-6.Simplify by combining like terms: Since m = 2x + 3, we can replace 14x with 7m - 21 because 14x = 7(2x) and 2x = m - 3. So, 7(2x) = 7(m - 3).Add 6 to both sides: Now we substitute 7m - 21 for 14x in the equation: (m)^(2) - (7m - 21) - 21 = -6.Next, we simplify the equation by combining like terms: (m)^(2) - 7m + 21 - 21 = -6.The +21 and -21 cancel each other out, so we are left with: (m)^(2) - 7m = -6.To get the equation in the standard form, we add 6 to both sides of the equation: (m)^(2) - 7m + 6 = 0.We have now found the equivalent equation in terms of m, which is (m)^(2) - 7m + 6 = 0. This corresponds to answer choice (C).

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Math Problems

Algebra 1

Solve a quadratic equation by factoring

Full solution

Q. Let

m=2x+3

. Which equation is equivalent to

(2x+3)^{2}-14x-21=-6

in terms of

m

? Choose

1

answer:

\newline

(A)

m^{2}+7m+6=0

\newline

(B)

m^{2}-7m-15=0

\newline

(C)

m^{2}-7m+6=0

\newline

(D)

m^{2}+7m-15=0

Substitute $m$ into equation: We are given $m = 2x + 3$ . Let's substitute $m$ into the given equation $(2x+3)^{2}-14x-21=-6$ to find the equivalent equation in terms of $m$ .
Replace $14x$ with $7m$ : First, we substitute $m$ into the equation: $(m)^{2}-14x-21=-6$ .
Simplify by combining like terms: Since $m = 2x + 3$ , we can replace $14x$ with $7m - 21$ because $14x = 7(2x)$ and $2x = m - 3$ . So, $7(2x) = 7(m - 3)$ .
Add $6$ to both sides: Now we substitute $7m - 21$ for $14x$ in the equation: $(m)^{2} - (7m - 21) - 21 = -6$ .
Add $6$ to both sides: Now we substitute $7m - 21$ for $14x$ in the equation: $(m)^{2} - (7m - 21) - 21 = -6$ .Next, we simplify the equation by combining like terms: $(m)^{2} - 7m + 21 - 21 = -6$ .
Add $6$ to both sides: Now we substitute $7m - 21$ for $14x$ in the equation: $(m)^{2} - (7m - 21) - 21 = -6$ .Next, we simplify the equation by combining like terms: $(m)^{2} - 7m + 21 - 21 = -6$ .The $+21$ and $-21$ cancel each other out, so we are left with: $(m)^{2} - 7m = -6$ .
Add $6$ to both sides: Now we substitute $7m - 21$ for $14x$ in the equation: $(m)^{2} - (7m - 21) - 21 = -6$ .Next, we simplify the equation by combining like terms: $(m)^{2} - 7m + 21 - 21 = -6$ .The $+21$ and $-21$ cancel each other out, so we are left with: $(m)^{2} - 7m = -6$ .To get the equation in the standard form, we add $6$ to both sides of the equation: $(m)^{2} - 7m + 6 = 0$ .
Add $6$ to both sides: Now we substitute $7m - 21$ for $14x$ in the equation: $(m)^{2} - (7m - 21) - 21 = -6$ .Next, we simplify the equation by combining like terms: $(m)^{2} - 7m + 21 - 21 = -6$ .The $+21$ and $-21$ cancel each other out, so we are left with: $(m)^{2} - 7m = -6$ .To get the equation in the standard form, we add $6$ to both sides of the equation: $(m)^{2} - 7m + 6 = 0$ .We have now found the equivalent equation in terms of $m$ , which is $(m)^{2} - 7m + 6 = 0$ . This corresponds to answer choice (C).