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+6=0 (C) m^(2)+7m-15=0 (D) m^(2)-7m-15=0

Given substitution equation: We are given the substitution m = 2x + 3. We need to find an equivalent equation for the expression (2x+3)^(2) - 14x - 21 = -6 in terms of m.Expand and simplify expression: First, let's expand the expression (2x+3)^(2) - 14x - 21 and simplify it. (2x+3)^(2) - 14x - 21 = (2x+3)*(2x+3) - 14x - 21 = 4x^2 + 6x + 6x + 9 - 14x - 21 = 4x^2 + 12x - 14x + 9 - 21 = 4x^2 - 2x - 12Equation simplification: Now, we equate the simplified expression to -6, as given in the original equation. 4x^2 - 2x - 12 = -6Isolate terms and replace: To find the equivalent equation in terms of m, we need to isolate the terms with x and replace them with m. Let's add 6 to both sides of the equation to simplify it further. 4x^2 - 2x - 12 + 6 = -6 + 6 4x^2 - 2x - 6 = 0Substitute x in terms of m: Now, we can substitute m for 2x + 3 in the equation. Since m = 2x + 3, we can solve for x in terms of m: 2x = m - 3 x = (m - 3) / 2Simplify equation with substitution: We substitute x in the equation 4x^2 - 2x - 6 = 0 with the expression we found in terms of m. 4*((m - 3) / 2)^2 - 2*((m - 3) / 2) - 6 = 0Combine like terms: Now, we simplify the equation by squaring the term and multiplying through by 4. 4*((m^2 - 6m + 9) / 4) - (2m - 6) - 6 = 0 (m^2 - 6m + 9) - (2m - 6) - 6 = 0We continue to simplify the equation by combining like terms. m^2 - 6m + 9 - 2m + 6 - 6 = 0 m^2 - 8m + 9 = 0

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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+6=0
(C) m^(2)+7m-15=0
(D) m^(2)-7m-15=0

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

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Q. Let

m=2 x+3

\newline

Which equation is equivalent to

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

in terms of

m

\newline

Choose

1

answer:

\newline

(A)

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

\newline

(B)

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

\newline

(C)

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

\newline

(D)

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

Given substitution equation: We are given the substitution $m = 2x + 3$ . We need to find an equivalent equation for the expression $(2x+3)^{2} - 14x - 21 = -6$ in terms of $m$ .
Expand and simplify expression: First, let's expand the expression $(2x+3)^{2} - 14x - 21$ and simplify it. $\newline$ $(2x+3)^{2} - 14x - 21 = (2x+3)\cdot(2x+3) - 14x - 21$ $\newline$ $= 4x^2 + 6x + 6x + 9 - 14x - 21$ $\newline$ $= 4x^2 + 12x - 14x + 9 - 21$ $\newline$ $= 4x^2 - 2x - 12$
Equation simplification: Now, we equate the simplified expression to $-6$ , as given in the original equation. $\newline$ $4x^2 - 2x - 12 = -6$
Isolate terms and replace: To find the equivalent equation in terms of $m$ , we need to isolate the terms with $x$ and replace them with $m$ . Let's add $6$ to both sides of the equation to simplify it further. $\newline$ $4x^2 - 2x - 12 + 6 = -6 + 6$ $\newline$ $4x^2 - 2x - 6 = 0$
Substitute $x$ in terms of $m$ : Now, we can substitute $m$ for $2x + 3$ in the equation. $\newline$ Since $m = 2x + 3$ , we can solve for $x$ in terms of $m$ : $\newline$ $2x = m - 3$ $\newline$ $x = \frac{m - 3}{2}$
Simplify equation with substitution: We substitute $x$ in the equation $4x^2 - 2x - 6 = 0$ with the expression we found in terms of $m$ . $4\left(\frac{m - 3}{2}\right)^2 - 2\left(\frac{m - 3}{2}\right) - 6 = 0$
Combine like terms: Now, we simplify the equation by squaring the term and multiplying through by $4$ . $4\times\left(\frac{m^2 - 6m + 9}{4}\right) - (2m - 6) - 6 = 0$ $\left(m^2 - 6m + 9\right) - (2m - 6) - 6 = 0$
Combine like terms: Now, we simplify the equation by squaring the term and multiplying through by $4$ . $\newline$ $4\times\left(\frac{m^2 - 6m + 9}{4}\right) - (2m - 6) - 6 = 0$ $\newline$ $(m^2 - 6m + 9) - (2m - 6) - 6 = 0$ We continue to simplify the equation by combining like terms. $\newline$ $m^2 - 6m + 9 - 2m + 6 - 6 = 0$ $\newline$ $m^2 - 8m + 9 = 0$